f.5 permutation

銀雞

2013-04-07 3:11 am

5 female and 4 male are lining up in a row for a group photo

a)if the male must not all stand together,find the number of possible arrangemen
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b)if the male must be seperated,find the number of possible arrangement

回答 (1)

用戶26240

2013-04-07 7:33 am

✔ 最佳答案

5.
a)
If the 9 persons are lining up without restriction :
The number of arrangements
= 9P9

If the males all stand together :
The 4 males form a group in row (internal permutations = 4P4).The group and the 5 females are then lining up in a row (6P6).
The number of arrangements
= 4P4 x 6P6

If the males do not all stand together :
The required number of arrangements
= 9P9 - 4P4 x 6P6
= 9! - 4! x 6!
= 345600

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b)
If the males are separated :
Firstly arrange the 5 females in a row (5P5) as :_F_F_F_F_F_
Then put the 4 males in 4 "_" out of the 6 "_" (6P4).

The required number of arrangements
= 5P5 x 6P4
= 5! x (6!/2!)
= 43200

參考: 土扁

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