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

Question

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 10 female board members and 20 male board members.

How many ways are there to make a committee of 20 board members?

How many ways are there to make a committee of 20 board members if exactly 3 must be female?

Answer 2

32 students in all, so 32C18 ways to make a committee
Using the criteria given, there would be 7C5 * 10C6 * 7C4 * 8C3 ways

similarly for the board, 30C20 or 10C3 * 20C17

Answer 3

There are 13 female board members and 17 male board members.

How many ways are there to make a committee of 18 board members?

How many ways are there to make a committee of 18 board members if exactly 6 must be female?

Answer 4

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

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