# Combinations Problem

## Homework Statement

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?

## Homework Equations

$$_n{C}_r=\frac{n!}{(n-r)!r!}$$

## 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?