6 freshmen, 6 sophomores, 6 juniors, and 6 seniors are
eligible to be on a committee.
In how many ways can a dance committee of 13 students
be chosen if it is to consist of exactly 2 juniors and
exactly 3 seniors, and the rest must be freshman or
sophomores?
Since there must be 2 juniors and 3 seniors, that's 5
of the 13, so that leaves 8 to be chosen from the 12
freshmen and sophomores.
That's
6 juniors choose 2
times
6 seniors choose 3
times
12 freshmen & sophomores choose 8
or (6C2)(6C3)(12C8) = (15)(20)(495) = 146500 ways.
Edwin