Question

A committee consists of 8 men and 11 women. In how many ways can a subcommittee of 4 men and 7 women be chosen

Answer 1

23100 ways

Explanation:

We have 8 men and 11 women

Number of ways of choosing a subcommittee of 4 men and 7 women

8C4 x 11C7

8!/(8-4)!4! x 11!/(11-7)!7!

= 8!/4!4! x 11!/4!7!

= (40320/24*24) x (39916800/24x5040)

= (40320/576) x (39916800/120960)

=70 x 330

= 23100 ways

We can select a subcommittee of 4 men and 7 women in 23100 ways.