Question

A committee must be formed with 5 teachers and 3 students. If there are 10 teachers

to choose from, and 13 students, how many different ways could the committee be
made?

Answer 1

72,072

Explanation:

To determine the number of different ways the committee can be formed, we need to calculate the combination of selecting 5 teachers out of 10 and 3 students out of 13.

The number of ways to choose 5 teachers out of 10 is given by the combination formula:

C(10, 5) = 10! / (5! * (10 - 5)!) = 252

Similarly, the number of ways to choose 3 students out of 13 is:

C(13, 3) = 13! / (3! * (13 - 3)!) = 286

To find the total number of ways the committee can be formed, we multiply the number of ways to choose teachers by the number of ways to choose students:

Total number of ways = 252 * 286 = 72,072

Therefore, there are 72,072 different ways the committee can be formed.