A school dance committee is to consist of 2 freshmen 3 sopho

A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 5 freshmen, 8 sophomores, 9 juniors, and 9 seniors are eligible to be on the committee, in how many ways can the committee be chosen? Your answer is:

Solution

2 freshmen can be chosen in C(5,2)

3 sophomores can be chosen in C(8,3)

4 juniors can be chosen in C(9,4)

5 seniors can be chosen in C(9,5)

So total number of ways committee can be chosen is

C(5,2)C(8,3)C(9,4)C(9,5)=8890560