Chapter 11 - Counting Methods and Probability Theory - 11.2 Permutations - Exercise Set 11.2 - Page 702: 64

This makes sense.

The number of possible permutations if r items are taken from n items is: nPr = $\frac{n!}{(n-r)!}$ The above formula makes sense because the order matters for the batting lineup, so all possible 9 player combinations must be considered.