# How do I solve the following combinations problem?Seven people are applying for two vacant school board positions; four are women, three are men. In how many ways can these vacancies be filled 1....

How do I solve the following combinations problem?

*Seven people are applying for two vacant school board positions; four are women, three are men. In how many ways can these vacancies be filled*

* 1. With any two applicants?*

* 2. With ony women?*

* 3. With one man and one woman?** *

### 1 Answer | Add Yours

A combination has no repetition and the order does not matter. The theorem is...

n! / r!(n-r)!

where **n **is the number of things to choose from and you choose **r** of them.

n = 7 applicants

r = 2 vacancies

7! / 2!(7-2)! = **21 ways**