Answer
There are $1,816,214,400$ different batting orders.
Work Step by Step
The order in which the players are selected is important. It is a permutation of 9 players from a group of 15 players.
$_{15}P_9=\frac{15!}{(15-9)!}=\frac{15\times14\times13\times12\times11\times10\times9\times8\times7\times6!}{6!}=1,816,214,400$
