Question

8 freshmen, 9 sophomores, 9 juniors, and 7 seniors are eligible to be on a committee.

In how many ways can a dance committee be chosen if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors.

Answer 1

Answer: 11113200

Explanation:

We know that , the number of combination of choosing r things from n things is given by :-

`^nC_r=(n!)/(r!(n-r)!)`

Then , the number of ways to choose a dancing committee if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors :-

Then , the number of ways to choose a dancing committee if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors :-

Then , the number of ways to choose a dancing committee if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors :-

`^8C_4* ^9C_5*^9C_2*^7C_3`

`=(8!)/((8-4)!4!)*(9!)/((9-5)!5!)*(9!)/((9-2)!2!)*(7!)/(3!(7-3)!)\\\\ =(8*7*6*5*4!)/(4!4!)*(9*8*7*6*5!)/(4!5!)*(9*8*7!)/(7!2!)*(7*6*5*4!)/(3!4!)\\\\=11113200`

∴ The number of ways to choose a dancing committee if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors = 11113200