Question

Please Help! This is Combinations

6 freshmen, 5 sophomores, 6 juniors, and 7 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 4 juniors and exactly 2 seniors, and the rest must be freshman or sophomores?

Answer 1

103950

Explanation:

ii)Total ways of selecting 2 seniors from 7 is 7c2

and Total ways of selecting 4 juniors from 6 is 6C4

selecting rest 7 from 5 sopho and 6 fresh is 11C7

now, total way of selection came to be as,

7C2×6C4×11C7

=21×15×330

=103950