A committee of 4 members is to be formed by selecting out of 6 man and 5 women. In how many different ways the committee can be formed if it should have 2 men and 2 women?

Question: A committee of 4 members is to be formed by selecting out of 6 man and 5 women. In how many different ways the committee can be formed if it should have 2 men and 2 women?Solution:2 men can be selected out of 6 men in 6C2 = 6!/2!(6 - 2)! = 15 waysAnd2 women can be selected out of 5 women in 5C2 = 5!/2!(5 - 2)! = 10 ways ∴ Required number of ways = 15 × 10 = 150∴ 150 different ways to form the committee with 2 men and 2 women.