# Homework Help: Combinations Problem

1. May 19, 2008

### temaire

1. The problem statement, all variables and given/known data
There are three girls and six boys on the school softball team. The team consists of a pitcher, a catcher, four infielders, and three outfielders. How many ways can the nine different positions be filled if the pitcher must be a girl and the catcher must be a boy?

2. Relevant equations
$$_n{C}_r=\frac{n!}{(n-r)!r!}$$

3. The attempt at a solution
The answer to this problem is $$(_3{C}_1)(_6{C}_1)(7!)$$. However, can someone explain the 7! part?

2. May 19, 2008

### Tedjn

The 7! refers to how many ways you can assign the 7 remaining people to the infield and outfield positions after assigning a girl and a boy to be pitcher and catcher.

3. May 19, 2008

### temaire

This is what I had thought. However, there are two positions not one, that the rest are assigned to. Doesn't that affect the answer?

4. May 19, 2008

### Tedjn

I'm assuming each of the infield and outfield positions are considered different (e.g. left field, right field, center field...)

5. May 20, 2008

### temaire

Thanks Ted, that's exactly what I was looking for.