Question

A baseball team’s roster consists of 25 players with 13 position players and the rest being pitchers. The team’s batting order for a particular game consists of 9 players. The first 8 places in the batting order are taken by position players. The last place is taken by a pitcher. How many batting orders are possible? Use the formula for permutations to find your answer.
15,444
2,042,975
51,891,840
622,702,080

Answer 1

First 8 spots: choose and arrange 8 of the 13 position players — P(13,8) = 13!⁄5! = 51,891,840.
Last spot: choose 1 of the 12 pitchers = 12.

Total = P(13,8) × 12 = 51,891,840 × 12 = 622,702,080.