Question

A judiciary committee of 5 is to be selected from a group of 5 democrats and 6 republicans, in such a way that there are at least two members from each party on the subcommittee. determine the number of ways that this subcommittee can be chosen.

Answer 1

What are the options? Note that "and" means multiply and "or" means addition

(2 democrats and 3 republicans) OR (3 democrats and 2 republicans)

5 x 4 x 6 x 5 x 4 + 5 x 4 x 3 x 6 x 5

20 x 120 + 60 x 30

2400 + 1800

40,000

Answer: 40,000