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