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by mandeepak » Tue Oct 30, 2007 12:08 pm
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?

A. 20
B. 40
C. 50
D. 80
E. 120

OA - D
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by ri2007 » Tue Oct 30, 2007 3:37 pm
Total number of ways 3 people can be selected (out of 10) is 10C3 = 120
Number of ways 1 couple can be selected (out of 5) = 5C1 = 5
Number of ways the 3rd person can be selected (out of 8) = 8C1 = 8
Total ways in which 3 people can be selected (which includes 1 couple) = 5*8 = 40

Total number of ways 3 people can be selected which does not have any couple = 120 - 40 = 80
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