SOLUTION: 6 freshmen, 5 sophomores, 7 juniors, and 7 seniors are eligible to be on a committee. In how many ways can a dance committee of 15 students be chosen if it is to consist of exac

Question 1019519: 6 freshmen, 5 sophomores, 7 juniors, and 7 seniors are eligible to be on a committee.
In how many ways can a dance committee of 15 students be chosen if it is to consist of exactly 2 juniors and exactly 4 seniors, and the rest must be freshman or sophomores?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
There are C(7,2) = 21 ways of choosing 2 from 7 juniors.
There are C(7,4) = 35 ways of choosing 4 from 7 seniors.
After choosing 6 people, we have to choose 9 more students from the 6 freshmen and 5 sophomores.
There are C(6,6)*C(5,3)+C(6,5)*C(5,4)+C(6,4)*C(5,5) = 10+30+15 = 55.
Thus there are 21*35*55 = 40,425 ways to choose.

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