急! M&S Permutation&Combination

humanbeing

2010-08-15 9:55 pm

At a school sport day, the timekeeper group for running events consists of a chief judge, 1 referee and 10 timekeepers. The chief judge and the referee are chosen from 5 teachers while the 10 timekeepers are selected from 16 students.If the probability of having a timekeeping group with all the timekeepers being boys is 3/364, find the number of boys among the 16 students.

thx

更新1:

係 ...all the timekeepers being boys is 3/364, ...

更新2:

can u explain the steps as well? i cannot really understand it

回答 (1)

用戶2053

2010-08-15 10:18 pm

✔ 最佳答案

Let x be the number of boys among the 16 students.The probability of having a timekeeping group with all the timekeepers being boys =x/16 * (x-1)/15 * (x-2)/14 * ... * (x-9)/7 = 3/364x(x-1)(x-2)...(x-9) = 3/364 * 16!/6! x! / (x-10)! = 239500800consider that x >= 10 ,x = 12There are 12 boys among the 16 students.

2010-08-15 15:00:46 補充：
16人抽10個人要10個都是boys,

第一個boys機會 : x/16

剩 15 人 , x - 1 個boys ,

第二個又是boys機會 : (x-1)/15

第三個又是boys機會 : (x-2)/14

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