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?

 

Expert Answers
samhouston eNotes educator| Certified Educator

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