Question

How many ways can a batting order of 9 baseball players be made from a team of 11?

Answer 1

Since it's the order you're working out, the order in which you pick the players play a huge role. Thus, this is a permutation question.
Since you're picking 9 people from 11 players, the formula goes like this: $^{11}P_9 = \frac{11!}{(11 - 9)!} = 19958400$ different ways.