combination& permutation

👨🏻‍🏫 學術台數學

[匿名]

2011-05-19 6:41 am

4 people are selected to play a game. Find the no. of ways to select these 4 people if
(i) there is no couple
(ii) there is exactly one couple

更新1:

total : 5 couple

更新2:

there are 5 couple in total , then 4 people are selected to play a game. Find.............................................................

回答 (3)

myisland8132

2011-05-20 8:10 am

✔ 最佳答案

4(I) Select 4 couples from 5 couples and then select one people from each couple. No. of ways = C(5,4) * 2^4 = 80

(ii) Select 1 couple from 5 couples. Then select 2 couples from 4 couples and select one people from each couple. No. of ways = C(5,1) * C(4,2) * 2^2 = 120

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破舊立新

2011-05-19 10:32 pm

4(i) Number of ways: 4! = 4 x 3 x 2 = 24

(ii) First, a couple is for a unit (2!), and grouped by the other 2 people, we have (2 + 1)! ways. And the couple still have 2! ways to select.

Number of ways: (2 + 1)! x 2! = 3! x 2! = 12

2011-05-19 23:33:59 補充：
4 people are selected by 5 couple to play a game？

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匿名

2011-05-19 7:20 am

In total how many people are there?

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