A baseball team has 25 total players consisting of 15 position players and 10 pitchers. How many dif

A baseball team has 25 total players consisting of 15 position players and 10 pitchers. How many different ways are there to arrange the batting order of 9 starting players if only one pitcher is used at a time and the pitcher always bats last.

(This means that 8 players are taken from the position players and one pitcher is then added at the end of the lineup.)

First 8 positions:
15P8 = 259,459,200

For the pitcher, we can have 10 different possibilities for the 9th player:
259,459,200 x 10 = 2,594,592,000 ways