Question

7 freshmen, 8 sophomores, 8 juniors, and 10 seniors are eligible to be on a committee.

In how many ways can a dance committee of 18 students be chosen?


In how many ways can a dance committee be chosen if it is to consist of 5 freshmen, 6 sophomores, 4 juniors, and 3 seniors.

Answer 1

There are 1,037,158,320 ways to choose a committee of 18 among 33 students.

There are 4,939,200 ways to choose 5 freshmen from 7, 6 sophomores from 8, 4 juniors from 8, and 3 seniors from 10.

Explanation:

33!/18!15! = 1,037,158,320

7!/5!2! * 8!/6!2! * 8!/4!4! * 10!/7!3!

= 7*3 * 7*4 * 7*5*2 * 10*4*3 = 4,939,200