Well, I think the book's answer may be wrong on this one. Here is my solution. Is this correct?

(15 choose 9) x 9! = 181681894400

"15 choose 9" represents the number of ways you can pick 9 players from the 15 on the roster, and 9! represents the possible ordered lineups. I multiplied them together because because we are matching one set of outcomes to the other set of outcomes.