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

From group of 10 men and 8 women committee of 8 members with not more than 5 men and not less than 5 women is formed in following ways. Case I. If 3 men and 5 men we selected number of ways = ¹⁰ C₃ ^8 C₅ = 10 9 8 3 2 8 7 6 5 4 5 4 3 2 1 =6720 Case II. If 2 men and 6 women are selected Number of ways = ¹⁰ C₂ ^8 C₆ = 10 9 2 8 7 6 5 4 3 6 5 4 3 2 =1260 Case III. If 1 man and 7 women are selected number of ways = ¹⁰ C₁ ^8 C₇=10 8=80 Case IV. If 0 men and 8 women are selected number of ways = ¹⁰ C₀ ^8 C₈=1 total number