10. A community of 3 people is to be selected from 5 married couples, such that the community does not include two people who are married to each other. How many such communities are possible?

(a) 40

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(b)120

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(d) 80

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Solution

The correct option is D
(d) 80

Ans: (d)
Sol: No. of ways to pick 3 individuals out of 5 couples such that a couple is included is 5C18C1 = 58 = 40

(Order of choice here doesn’t matter)

Total no. of ways to pick 3 people from ten = 10C3 = 1098/(3*2) = 120

Therefore ways to select 3 individuals out of 5 couples such that no couple is included = 120-40 = 80.

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