GWD 5-3 老题新问

Q3:

If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?   D

A.     20

B.     40

C.     50

D.     80

E.      120

这道题做了两次，第一次做对了，但是第二次做错了，这两次解题的步骤分别是：

第一次：先从5对夫妻中任选3对，就是C5，3   然后在从被选中的三对中每对抽出一个人就是2的3次方种选法  结合起来就是：C5,3 *（2 的三次方）答案是对的

第二次：我是先从5对夫妻中每对抽出一个人，共有2的5次方种选法，然后再从选中的5个任里在任选3人，就是C5，3     答案是错的

我就是想请教我第二次做的过程思路哪里错了，谢谢

your second attempt; 2^5(your choices) * C5,3(couples);  you included the choices from two couples you did not pick, those two couples you did not pick each has 2 choices which would compute to 2^2, thats your extra factor

you should exclude it

先从5对夫妻中每对抽出一个人，共有2的5次方种选法，然后再从选中的5个任里在任选3人

就是你把另外沒選上的兩人的選法也算進去了