The manager of a baseball team has 15 players to choose from for his 9 person batting order

Given the question:
The manager of a baseball team has 15 players to choose from for his 9-person batting order. How many different ways can he arrange the players in the lineup?
5,005    362,880    3,603,600    1,816,214,400

The number of was in which a smaller group is choosing from a bigger group is given by the bigger number combination the smaller number.

Here, we want to choose a 9-person batting order from a team of 15 players. This is given by: