Probability question

gastank · 发表于 2012-1-22 01:26:18

To select 3 people to be on a committee from 4 married couples, and the 3 people selected can not be married to each other. What is the number of different committees?

a. 16
b. 24
c. 26
d. 30
e. 32

Thanks.

WhiteSuby · 发表于 2012-1-22 02:05:09

You have 4 married couples; this is equivalent of 8 people. And you want to choose 3 people:
First Round: 8 selections
Second Round: 6 selections (refer to restriction from question stem; cannot have married couple in there)
Third Round: 4 selections (same as above)
Total: 8x6x4
Because matter does not matter here, this is a combination question, then you need to divide 3!
8x6x4/3*2*1=32

脆脆 · 发表于 2012-1-22 13:51:31

我觉得是C
C3,8-5*C2,4

gastank · 发表于 2012-1-22 22:43:43

答案是32.

la2ny · 发表于 2012-7-5 11:26:50

can you please explain why we divide by 3! ? Is it b/c the 3 chosen ones are not organized in any particular order?

Also, what level would you say this question is? It's challenging, i would think 700-800.

depressedfrog · 发表于 2012-7-5 23:59:57

C3,8-C1,4C1,6 =32
先从8人中选3人共有C3,8种选法减去任何有COUPLE出现的情况C1,4C1,6 剩余就是没有couple出现的情况

silcdedicate · 发表于 2012-7-6 00:11:25

c83- c41 X （8-2）= 32 种反过来想就好了

Probability question

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