Question

If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include a married couple, how many such committee are possible. A) 20 B) 40 C) 50 D) 80 E) 120

Answer 1

option D.

Explanation:

given,

5 married couples and we have to form the committee of 3 people such that no married couple comes together in the committee.

total number of people present = 5 × 2 = 10 people

selecting 3 people randomly = ¹⁰C₃ = 120 ways

number of ways of selecting couple = ¹⁰C₁× ⁴C₁

= 40 ways

so, ways to select committee which does not include married couple =

= 120 - 40 = 80 ways

so, the correct answer is option D.