Question

A committee consists of 8 men and 11 women. In how many ways can a subcommittee of 3 men and 5 women be chosen?

Answer 1

25872 ways

Explanation:

We're choosing 5 women from a group of 11 and 3 men from a group of 8. We don't care about what order they are picked and so we'll use the combination formula, which is:

n!/(k!)(n-k)! with n as population and k as picks.

We'll multiply the results together. (8! / (3!)(8-3)!) * (11! / (5!)(11-5)!)

That equals: (8! / (3!)(5!) ) * (11! / (5!)(6!)) = 40320/(6x120) * 39916800/ (120x720)

56 * 462 = 25872