From a group of 10 men and 8 women, the number of ways of forming a committee of 8 members with not more than 5 men and not less than 5 women is

Step-by-step solution

Given, 1   Group→ 10   Men 8  Women We want to form a committee such that 1   Committee→ ≤ 5   Men ≥ 5  Women Total ways of forming a committee of 8 members with not more than 5 men and not less than 5 women are = 5 W ,   3 M + 6 W ,   2 M + 7 W ,   1 M + 8 W ,   0 M = C 5 8 × C 3 10 + C 6 8 × C 2 10 + C 7 8 × C 1 10 + C 8 8 × C 0 10 = 8061 ways.