Question

6 freshmen, 5 sophomores, 6 juniors, and 5 seniors are eligible to be on a committee. In how many ways can a dance committee of 16 students be chosen if it is to consist of exactly 4 juniors and exactly 3 seniors, and the rest must be freshmen or sophomores

Answer 1

24750

Explanation:

Given that 6 freshmen, 5 sophomores, 6 juniors, and 5 seniors are eligible to be on a committee

16 students be chosen if it is to consist of exactly 4 juniors and exactly 3 seniors, and the rest must be freshmen or sophomores

i.e. dance committee will have 16 students out of which

4 juniors 3 seniors 8 freshmen or sophomores from

6 juniors, 5 seniors and 5 sophomores and 6 freshmen

Junior can be selected in 6C4 = 15 ways

Seniors in 5C3 = 10 ways

Freshman or sophomores in 11C8 = 165

The total no of ways = product of these three

=
`15*10*165\\= 24750`