Question 1019517
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?
<pre>
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</pre>