From a group of 7 men 6 women, 5 persons are to be selected to form a…

Question

From a group of 7 men 6 women, 5 persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

Accepted Answer

Option D. 756. Answer & Solution Answer: Option D Solution: Required number of ways = ( ^7C_3 × ^6C_2 ) + ( ^7C_4 × ^6C_1 ) + ( ^7C_5 × ^6C_0 ) = \ 7 × 6 × 53! × 6 × 52! \ + ( ^7C_3 × ^6C_1 ) + ( ^7C_2 × 1 ) = \ 7 × 6 × 56 × 6 × 52 × 1 \ + ( 7 × 6 × 53 × 2 × 1 × 6 ) + ( 7 × 62 × 1 × 1 ) & = (…