Statistics Question

Question

How many ways can a committee of 2 faculty members and 3 students be selected from 7 faculty members and 8 students? Show your work.

Answer 1

Let’s do a similar problem: how many ways can a committee of 3 faculty members and 2 students be selected from 8 faculty members and 5 students?

There are 2 actions needed to select our committee: 1) select 3 faculty members from the set of 8 faculty members, and 2) select 2 students from the set of 5 students. No order is needed in these two actions. That is to say, we can first do action 1, then do action 2, or vice verse. In addition, there is no dependency between these 2 actions.

Hence, if we find out that there are F number ways to take action 1, and there are S number ways to take action 2, then we will have F * S number ways to select our committee.

So, to solve the problem, we need to find out the number F and the number S.

You may notice that from the perspective to solve the math problem, they are the exactly same kind of math problem to find F and to find S. If we know how to find the number F for action 1, we know how to find the number S for action 2. The nature of the 2 actions are the same.

Let’s now do F for action 1: how many ways can we select 3 faculty members from 8 faculty members? This is a math problem in combination. We solve this kind of math problem by combination formula C(8, 3) = 8! / (5! 3!) = 56.

Similarly, we can get S = C(5, 2) = 10.

Then, the number of ways to select our committee is F * S = 56*10 = 560.