Answer
See below.
Work Step by Step
If we want to choose $k$ elements out of $n$ regarding the order, not allowing repetition, we can do this in $_{n}P_k=\frac{n!}{(n-k)!}$ ways.
The order matters here when choosing the batters, thus we have to use permutations. We have $9$ people for $9$ spots, thus $_{9}P_{9}=\frac{9!}{(9-9)!}=9!=362880$
