a group of 7 females and 13 males volunteer for a medical study. how many selections can be made for 4 volunteers if there is at least 1 male? at most 1 female?

Answer 1

I found it helpful to break down a couple of different possibilities. If all we know is that there are 4 volunteers who are either male or female, then you could have:

4 males

3 males, 1 female

2 males, 2 females

1 male, 3 females

4 females.

But since we are told that there is at least one male and at most 1 female, only the first two rows are possible. So basically we have two cases to consider:

How many ways are there to choose 4 males out of 13? C(13,4)

And how many ways are there to chose 1 female out of 7 and at the same time choose 3 males out of 13?

7 • C(13,3)

So to find the answer you just need to calculate:

C(13,4) + 7 • C(13,3)