Permutation & Combination

[匿名]

2011-04-04 3:15 am

Ten cards marked 1 to 10. Find the number of ways to group them into 5 pairs.

更新1:

To : ☂雨後陽光☀ 請各位發表回答前先備份以免遇上發表故障被清空內容. Please explain why divided by 5!.

回答 (1)

用戶2053

2011-04-04 3:34 am

✔ 最佳答案

(10C2)(8C2)(6C2)(4C2)(2C2) / 5!= 45 * 28 * 15 * 6 * 1 / 120= 945 ways.

2011-04-03 19:44:29 補充：
Consider a simple case then you will understand :

Four cards marked 1 to 4

1 , 2 , 3 , 4

Number of ways to group them into 2 pairs

= (4C2) (2C2) / 2! = 3 ways
i.e.
12 , 34
13 , 24
14 , 23
(3 cases)

2011-04-03 19:44:36 補充：
For each case , using 12 , 34 for example :
(4C2) (2C2) may be 12 and then 34 or 34 and then 12 , (2! cases)

So the number of ways = (4C2) (2C2) / 2!

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