Question

A committee must be formed with 3 teachers and 3 students. If there are 10 teachers to choose from, and 9 students, how many different ways could the committee be made?

Answer 1

10080 ways

Explanation:

First we find the amount of combinations of teachers who can be chosen, which is denoted by 10 choose 3 (10 nCr 3), shown below:

10! / (3! * 7!) --> 120

Next to find the amount of combinations of students, you evaluate 9 choose 3(9 nCr 3), shown below:

9! / (3! * 6!) --> 84

To find the total number of combinations, you multiply the teachers combinations by the students combinations:

120 * 84 = 10080