兩題數，唔知有無計錯，請指點一下

2010-05-12 9:28 am

圖片參考：http://imgcld.yimg.com/8/n/HA00207615/o/701005120010113873410410.jpg

a . = 8! = 40320

b .= 3! x 5! x 6 = 4320

c .= no way to be arranged

圖片參考：http://imgcld.yimg.com/8/n/HA00207615/o/701005120010113873410411.jpg

a. = ( 10! / 5! ) x ( 12! / 6! ) = 30240 x 665280 = 20118067200

b. = 3! = 6

c. = (12! / 6! ) + { ( 12! / 7! ) x ( 10! / 9! ) } + { ( 12! / 8! ) x ( 10! / 8! ) }

= 665280 + 950400 + 1069200 = 2684880

唔知有無解錯題，如有錯請題點，Thank You !

更新1:

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回答 (1)

用戶2053

2010-05-12 7:03 pm

✔ 最佳答案

個人愚見只供參考 :
1a) (3+5)! ways (No problem.)
1b) 3 maths books 當一件共 3! ways , 加上 5 computer books 共 6 件 ,
共 6! ways , Total 3! * 6! ways. (No problem)
1c) 3本maths 只有 4 個擺位 , 放不能完全分隔 5 本 computer books .
no way. (No problem)

2a) 10C5 * 12C6 = 10! / [5! (10-5)!] * 12! / [6! (12-6)!]
= 252 * 924 = 232848 ways

2b) The 1st boy have 3 girls choice , the 2nd boy have 2 girls choice , the 3rd boy have 1 girl choice ,
3 x 2 x 1 = 3! (No problem)

2c) The number of ways
= (4 girls , 2 boys)ways + (5 girls , 1 boy)ways + (6 girls) ways
= 12C4 * 10C2 + 12C5 * 10C1 + 12C6
= 12! / [4! (12-4)!] * 10! / [2! (10-2)!] + 12! / [5!(12-5)!] * 10 + 12! / [6!(12-6)!]
= 495*45 + 792*10 + 924
= 31119 ways

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