Question

Please help asap, Combinations :(

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 14 students be chosen if it is to consist of exactly 3 juniors and exactly 2 seniors, and the rest must be freshman or sophomores?

Answer 1

66000

Explanation:

Total ways of selecting 2 seniors from 6 is 6C2

and Total ways of selecting 3 juniors from 6 is 6C3

ways of selecting rest 9 from 12 sopho or fresh is 12C9

now, total way of selection come to be

12C9×6C3×6C2

i.e, 220×20×15

i.e, 66000