SOLUTION: 5 freshmen, 5 sophomores, 5 juniors, and 5 seniors are eligible to be on a committee. In how many ways can a dance committee of 14 students be chosen if it is to consist of exac

Algebra ->  Permutations -> SOLUTION: 5 freshmen, 5 sophomores, 5 juniors, and 5 seniors are eligible to be on a committee. In how many ways can a dance committee of 14 students be chosen if it is to consist of exac      Log On


   

Question 1118366: 5 freshmen, 5 sophomores, 5 juniors, and 5 seniors are eligible to be on a committee.
In how many ways can a dance committee of 14 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 greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


4 of the 5 seniors: "5 choose 4" = C(5,4) = 5

AND

2 of the 5 juniors: "5 choose 2" = C(5,2) = 10

AND

8 of the 10 freshmen and sophomores: "10 choose 8" = C(10,8) = 45

Multiply the number of different ways to make the different selections to find the total number of ways:

5*10*45 = 2250