## Statistics: Informed Decisions Using Data (4th Edition)

$252$ different starting lineups.
- First, let's select Payton or Jordyn for goalie. We have two choices. $N(goalie)=2$ - Now, we need to select 4 fielders among the 9 remaining players: 1) It is not a sequence of choices. 2) The order in which the players are selected does not matter. It is a combination of 9 distinct players taken 4 at a time: $_{9}C_4=\frac{9!}{4!(9-4)!}=\frac{9!}{4!\times5!}=\frac{9\times8\times7\times6\times5\times4\times3\times2\times1}{4\times3\times2\times1\times5\times4\times3\times2\times1}=126$ Using the Multiplication Rule of Counting (page 298): $N(starting~lineups)=2\times126=252$