ความน่าจะเป็นเบื้องต้น(Propability)

เอกสารประกอบการเรียนวชิ าคณิตศาสตร์ หนา้ 1 เรื่อง ความน่าจะเป็ น ____________________________________________________________________________________________________________________________ ความนาจะเปน เบ้อื งตน 1. กฏเกณฑการนบั เบอื้ งตน คําชี้แจง ใหน ักเรียนพิจารณาตวั อยา งตอไปน้ี ตวั อยา งท่ี 1 ใน Audition Game ผูเ ลนจะสามารถแตงตัวใหก ับตวั ละครของตนเองไดตามใจชอบ ถาหาก ตวั ละครของเด็กชายคนหนึ่ง สามารถเลือกเส้ือได 3 ตัว และสามารถเลือกกางเกงได 2 ตวั อยากทราบวา ตวั ละครของเดก็ คนนีจ้ ะสามารถแตง ตวั ทงั้ หมดไดกแี่ บบ วธิ ีทํา จากแผนภาพจะเหน็ วา ตัวละครของเด็กชายคนนี้จะสามารถแตงตัวโดยมีเสอ้ื 3 ตัวและกางเกง 2 ตวั ไดท งั้ หมด ......................................แบบ ซ่ึงเทากบั จํานวนเส้อื ................... (ตวั ) คูณ ดว ยจาํ นวนกางเกง...................(ตัว) หรอื เทากับ...............×...............= ............... นัน่ เอง

เอกสารประกอบการเรียนวชิ าคณิตศาสตร์ หนา้ 2 เร่ือง ความน่าจะเป็ น ____________________________________________________________________________________________________________________________ ตวั อยา งท่ี 2 โดเรมอ นมีประตูกาลเวลาทั้งหมด 3 ประตู ถา โดเรมอ นสามารถเดนิ เขาและเดินออกประตู กาลเวลาใดก็ได จงหาวา โดเรมอ นจะมีวิธีเดินเขา และออกประตูกาลเวลานีไ้ ดทั้งหมดกว่ี ธิ ี วธิ ที ํา จากแผนภาพจะเห็นวา โดเรมอนจะสามารถเดินเขาและออกประตูวิเศษโดยมี 3 ประตู ไดท ัง้ หมด ...................วิธี ซง่ึ เทากับจํานวนประตูที่เดนิ เขา................... (ประต)ู คูณ ดว ยจาํ นวนประตูท่ีเดนิ ออก...................(ประต)ู หรอื เทากับ...............×...............= ............... นั่นเอง จากตัวอยา งที่ 1 และ 2 เราสามารถสรปุ เปน กฎ (ในกรณีท่ัวไป) ไดด ังน้ี หลกั การคูณ กฎข้อที่ 1 ..................................................................................................................................................................................................................... ............ ..................................................................................................................................................................................................................................................................

เอกสารประกอบการเรียนวชิ าคณิตศาสตร์ หนา้ 3 เร่ือง ความน่าจะเป็ น ____________________________________________________________________________________________________________________________ ตวั อยา งท่ี 3 มถี นนจากตาํ บล ก ไปตําบล ข อยู 5 สาย และมถี นนจากตําบล ก ไปตําบล ข อยู 3 สาย อยากทราบวาถาตองการเดนิ ทางจากตาํ บล ก ไปยังตําบล ค โดยผา นตาํ บล ข จะทาํ ไดทั้งหมดก่วี ิธี วธิ ที ํา ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ตัวอยางที่ 4 ในการทอดลูกเตาสองลกู จะปรากฎผลไดท ้ังหมดกวี่ ธิ ี วิธีทาํ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ตวั อยา งท่ี 5 ทาเรอื ขามแมนํ้าเจา พระยา มีเรอื ขามฟาก 5 ลํา ถานักเรยี นคนหนึ่งตองการขามฟากไปและกลบั จงหาจาํ นวนวธิ ีทน่ี กั เรยี นคนนี้จะเดินทางขา มฟากโดย 1) ไปและกลบั จะลงเรือลําใดก็ได 2) ไปและกลบั จะลงเรือซาํ้ ลําเดิมไมได 3) ไปและกลับลงเรือลาํ เดียวกัน วธิ ีทํา ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... .........................................................................................................................................................................................................................................................................

เอกสารประกอบการเรียนวชิ าคณิตศาสตร์ หนา้ 4 เร่ือง ความน่าจะเป็ น ____________________________________________________________________________________________________________________________ โดยการขยายกฎขอที่ 1 ใหใชกบั การทํางานหรือปฏิบตั ิการมากกวา 2 อยาง จะไดกฎทั่วไป ดังน้ี กฎข้อท่ี 2 ....................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................. ตวั อยางท่ี 6 เมอ่ื โยนเหรยี ญหน่ึงเหรียญหนึง่ ครง้ั เหรยี ญอาจข้นึ หัวหรือกอยก็ได อยากทราบวาถา โยน เหรยี ญหน่งึ เหรยี ญ 3 ครัง้ จะไดผ ลลัพธต างๆกันทั้งหมดก่ีวธิ ี วธิ ีทาํ สมมตใิ หH แทนการโยนเหรียญแลวขึน้ หัว T แทนการโยนเหรยี ญแลว ขึ้นกอย หาผลลัพธท้ังหมดโดยใชแผนภาพตน ไมดงั น้ี จากแผนภาพจะเหน็ วา งานน้ีแบงออกเปน 3 ขัน้ ตอน คอื ขนั้ ตอนท่ี 1 โยนเหรยี ญครงั้ ที่หนง่ึ จะได......................................วิธี ขน้ั ตอนท่ี 2 โยนเหรียญคร้งั ท่ีสองจะได. .....................................วธิ ี ข้ันตอนท่ี 3 โยนเหรียญคร้ังท่ีสามจะได. .....................................วิธี ดงั น้นั การโยนเหรียญหน่งึ เหรียญ 3 ครั้ง จะไดผลลพั ธต า งๆกนั ทั้งหมด......................................วิธี

เอกสารประกอบการเรียนวชิ าคณิตศาสตร์ หนา้ 5 เรื่อง ความน่าจะเป็ น ____________________________________________________________________________________________________________________________ ตัวอยางท่ี 7 รานคาจําหนายเสื้อผาสําเร็จรูป จําหนายเส้ือท้ังหมด 5 แบบ แตละแบบมี 4 สี และแตละสีมี 3 ขนาด ถาตองการจัดเสื้อโชวห นา รานใหครบทกุ สี ทุกขนาด จะตอ งเตรยี มไมแขวนเสอื้ ทัง้ หมดก่ีอัน วิธีทํา ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ตัวอยางท่ี 8 ถา ตอ งการสรา งจํานวนเตม็ บวกทีม่ ีสีห่ ลกั จากเลขโดด 0-9 จะสรางไดทง้ั หมดกี่จํานวน เมือ่ ตองการให 1) แตละหลักใชเ ลขซ้ํากันได 2) แตล ะหลกั ใชเลขซํ้ากนั ไมได วิธที าํ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... .........................................................................................................................................................................................................................................................................

เอกสารประกอบการเรียนวชิ าคณิตศาสตร์ หนา้ 6 เร่ือง ความน่าจะเป็ น ____________________________________________________________________________________________________________________________ ตวั อยางที่ 9 จะมวี ธิ ที แ่ี ตกตา งกนั ทง้ั หมดก่วี ธิ ที จี่ ะเลือกสี 8 สี มาทาลูกเตาหนา ละสี วิธีทํา ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ตวั อยา งท่ี 10 จงหาจํานวนวธิ ที เ่ี ปน ไปไดทัง้ หมดในการสง จดหมาย 4 ฉบับ ลงในตูไปรษณยี  5 ตู ถา ... - จดหมายแตละฉบับจะใสต ูใ ดกไ็ ด - หามใสจ ดหมายมากกวา 1 ฉบบั ในตเู ดียวกนั วธิ ีทํา ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... .........................................................................................................................................................................................................................................................................

เอกสารประกอบการเรียนวชิ าคณิตศาสตร์ หนา้ 7 เรื่อง ความน่าจะเป็ น ____________________________________________________________________________________________________________________________ แบบฝก ทักษะที่ 1.1 เรือ่ ง กฎเกณฑเบอ้ื งตน เกีย่ วกบั การนับ 1. นักเรียนคนหนึง่ ตองการเลือกเรยี นภาษาตา งประเทศ 1 ภาษา จาก 5 ภาษา และตองการเรียนวิชา วิทยาศาสตร 1 วชิ าจาก 4 วชิ า นักเรียนคนนีจ้ ะมวี ิธีเลือกเรียนไดท ง้ั หมดก่วี ธิ ี วธิ ที ํา ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... นักเรยี นหองหน่งึ มี 40 คน ตองการเลือกหวั หนา หองและรองหวั หนาหอง จะมวี ิธีเลอื กไดทง้ั หมดกี่วิธี วิธที ํา ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... มถี นนจากเมือง ก ไปยังเมอื ง ข 6 สาย และจากเมือง ข ไปยงั เมอื ง ค 4 สาย จงหาจํานวนวิธที ้ังหมดทีจ่ ะขบั รถยนต - จากเมือง ก ไปยังเมือง ค - จากเมือง ก ไปยังเมือง ค แลวขบั กลับ - จากเมืองก ไปยังเมือง ค แลว ขับกลับโดยไมขบั ผา นซํ้าในถนนสายเดียวกัน วธิ ีทาํ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... .........................................................................................................................................................................................................................................................................

เอกสารประกอบการเรียนวชิ าคณิตศาสตร์ หนา้ 8 เรื่อง ความน่าจะเป็ น ____________________________________________________________________________________________________________________________ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ถานาํ เลขโดด 0-4 มาสรางเปน จาํ นวนที่มสี องหลัก จะสรางไดท ้งั หมดกีจ่ าํ นวน ถา - ไมมเี ง่ือนไขใดๆ - แตล ะหลักเลขตองไมซ ้ํากัน วธิ ที าํ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... 2. มีนักเรียน 5 คน ตอ งการนํานักเรียนจาํ นวน 3 คนมายืนเรียงเปน แถว จงหาจาํ นวนวธิ ีทจี่ ะจดั ได ท้ังหมด วธิ ที ํา ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... .........................................................................................................................................................................................................................................................................

เอกสารประกอบการเรียนวชิ าคณิตศาสตร์ หนา้ 9 เร่ือง ความน่าจะเป็ น ____________________________________________________________________________________________________________________________ 3. จงนําตวั อักษรจากคําวา SPECIAL มาเรียงเปน คําใหมโดยไมคํานึงถึงความหมาย จะไดค ําไมท่ีไมซ ํ้ากับ คาํ เดมิ ท้ังหมดก่ีคํา วิธที าํ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... 4. ชมรมตน กลา คณติ ศาสตร ตองการเลอื กประธาน รองประธาน และเลขานกุ าร ตาํ แหนงละ 1 คน จาก ผสู มคั รทั้งหมด 8 คน จะมีวธิ เี ลอื กประธาน รองประธาน และเลขานกุ ารไดกว่ี ิธี ถามผี สู มคั รหน่ึงคนไม สมคั รใจเปน ประธาน วิธที าํ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... 5. ขอสอบวชิ าคณติ ศาสตรมคี ําถามแบบถูกผิด อยทู ้ังหมด 8 ขอ ตางๆ กนั ถาเด็กหญิงเดน จันทร ทาํ ขอ สอบวชิ านโี้ ดยการเดา เด็กหญิงเดน จันทรจ ะมีวธิ กี ารทําขอสอบทัง้ 8 ขอ ไดทงั้ หมดก่ีวธิ ี วธิ ีทาํ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... .........................................................................................................................................................................................................................................................................

เอกสารประกอบการเรียนวชิ าคณิตศาสตร์ หนา้ 10 เร่ือง ความน่าจะเป็ น ____________________________________________________________________________________________________________________________ 6. นกพริ าบ 5 ตวั จะเลือกบนิ มาเกาะตน ไม 3 ตนไดกว่ี ิธี วธิ ที ํา ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... 7. การโยนลูกเตาสองลูกท่ีแตกตางกนั ใหไดแ ตม คูทง้ั สองลกู ทําไดก ว่ี ิธี วธิ ที าํ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... 8. ในการทอดลูกเตา n ลกู พรอมกนั 1 ครั้ง จะปรากฏผลไดกี่วธิ ี วธิ ที ํา ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... .........................................................................................................................................................................................................................................................................

เอกสารประกอบการเรียนวชิ าคณิตศาสตร์ หนา้ 11 เรื่อง ความน่าจะเป็ น ____________________________________________________________________________________________________________________________ 9. รถยนตค ันหน่งึ มีท่ีนงั่ อยูขา งหนา (รวมทค่ี นขับ) 2 ท่ี และขางหลัง 3 ที่ ถามคี นงานท้ังหมด 7 คน ซ่ึง 3 คนขับรถได จะจัดคนเขา นั่งรถไดก่วี ิธี วิธที าํ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... .........................................................................................................................................................................................................................................................................

เอกสารประกอบการเรียนวชิ าคณิตศาสตร์ หนา้ 12 เร่ือง ความน่าจะเป็ น ____________________________________________________________________________________________________________________________ กฎข้อที่ 3 กฎโดยการบวก ........................................................................................................................................................................................................... ...................................................................................................................................................................................................................................................... ........................... ....................................................................................................................................................................................................................................................... .......................... ตัวอยางที่ 1 ถา หมายเลขทะเบียนรถยนตใ นกรงุ เทพมหานครประกอบดว ยพยญั ชนะ 2 ตัว และตวั เลข 1 ถงึ 4 หลกั ตัวอยา งเชน กข 1 , กค 12 , กง 123 และ กจ 1234 อยากทราบวา จะมีหมายเลขทะเบียนรถยนตท ่ี แตกตางกนั ท้ังหมดไดกห่ี มายเลข วธิ ีทาํ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ตัวอยา งที่ 2 จะจัดชาย 3 คน และหญิง 3 คนเขาแถวตรงไดกวี่ ธิ ี โดยใหช ายและหญิงยืนสลับกนั วิธีทาํ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... .........................................................................................................................................................................................................................................................................

เอกสารประกอบการเรียนวชิ าคณิตศาสตร์ หนา้ 13 เรื่อง ความน่าจะเป็ น ____________________________________________________________________________________________________________________________ ตัวอยา งท่ี 3 บานพักและสถานที่ทํางานของเพลิง ต้งั อยูร ิมแมนํา้ เจา พระยา เพลงิ โดยสารเรือยนตไ ปทาํ งาน ตอนเชา และกลับท่ีพกั ในตอนเย็น ถา เรือยนตม ี 3 มีขนาด คือ ขนาดใหญ 3 ลํา ขนาดกลาง 5 ลํา และ ขนาด เลก็ 2 ลาํ จงหาจํานวนวธิ ีทแี่ ตกตา งกันทง้ั หมดทเ่ี พลงิ โดยสานเรือยนตไ ปทํางานและกลับบานพกั ดว ยเรือขนาด เดยี วกนั แตไ มใ ชเ รอื ลําเดียวกัน วิธที าํ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ตัวอยา งที่ 4 กาํ หนดใหมีบตั ร 4 ใบ เขยี นหมายเลข 1 , 2 ,3 และ 4 นําบตั รเหลา นีม้ าเรียงเปน จาํ นวนตางๆ ดงั น้ีไดก ี่จํานวน วธิ ที าํ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... .........................................................................................................................................................................................................................................................................

เอกสารประกอบการเรียนวชิ าคณิตศาสตร์ หนา้ 14 เรื่อง ความน่าจะเป็ น ____________________________________________________________________________________________________________________________ แบบฝกทักษะท่ี 1.2 เรือ่ ง กฎเกณฑเบ้อื งตน เกีย่ วกบั การนบั 1. นกั เรียนกลุมหนึง่ มเี ดก็ ผชู าย 3 คน และเด็กผูหญงิ 4 คน จงหาจํานวนวิธเี ลอื กตวั แทน 2 คนที่มเี พศ เดียวกนั วิธีทาํ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... 2. ตอ งการนาํ เลขโดด 0-9 มาสรางเปนจาํ นวนเต็มคูบวก 3 หลกั โดยไมม เี ลขในหลักใดซํ้ากันเลย จะ สรา งจาํ นวนเตม็ บวกไดกจ่ี ํานวน วิธีทํา ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... 3. กําหนดใหใ ชต วั เลข 0,1,2,3,4,5,6 และ 7 สรางจํานวนที่มี 3 หลกั โดยกาํ หนดวาแตละหลักไมมี ตวั เลขซํา้ กัน จงหาวา จาํ นวนเลขสามหลกั ทเ่ี ปน เลขคู มีทั้งหมดกี่จํานวน วิธีทาํ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... .........................................................................................................................................................................................................................................................................

เอกสารประกอบการเรียนวชิ าคณิตศาสตร์ หนา้ 15 เรื่อง ความน่าจะเป็ น ____________________________________________________________________________________________________________________________ 4. จากตวั เลข 0, 1 , 2 , 3 , 4 และ 5 จะสรางจาํ นวนทม่ี ี 3 หลกั และจํานวนเหลานห้ี ารดว ย 5 ลงตัวจะ มีท้งั หมดกจ่ี ํานวน เมอื่ 4.1 ใชเลขซํ้าได 4.2 ใชเ ลขซ้าํ ไมได วธิ ที ํา ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... 5. จงหาจํานวนคี่ทอี่ ยูร ะหวาง 3,000 ถงึ 5,000 มีกีจ่ ํานวนโดยท่ีแตล ะหลกั มีตัวเลขแตกตางกัน วธิ ีทาํ ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................................... .........................................................................................................................................................................................................................................................................