The senate in a certain state is compromised of 58 republicans, 39 democrats, and 3 independents. How many committees can be formed if each committee must have 3Republicans and 2 Democrats?

Defining C (n, r) as the number of combinations (order does not count) to choose r objects from n, where C (n, r) = n! / (r! (n-r) !)

there are

C (58,3) ways to choose 3 from 58 republicans,

and

C (39,2) ways to choose 2 from 39 democrats.

So the committee has

(C (58,3) * (C (39,2)) variants, or

58! / (3!55!) * 39! / (2!37!)

=30856*741

=22864296