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A committee of 5 is to be chosen from 6 married couples so that no husband and wife are both on it. How many committees are possible?

Competition practicePermutations & Combinations

A792
B192
C32
D384

Step-by-Step Solution

Choose the 5 couples that send one member:

^{6} C_{5} = 6

. Each sends the husband or the wife:

2^{5} = 32.6 \times 32 = 192. (792 =^{12} C_{5}

ignores the rule.)

Answer: B) 192

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