19
QuizMultiple Choice

Finding Outcomes — Test

Question 19 • CR - Algebra 2 26-27 - S2

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.

Answer
A
15,444
B
2,042,975
C
51,891,840
D
622,702,080

Explanation

Arrange 8 of the 13 position players in the first 8 spots: P(13, 8) = 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 = 51,891,840. There are 25 − 13 = 12 pitchers, and any one of them can take the last spot. Thus, the total is 51,891,840 × 12 = 622,702,080 batting orders, which is choice D.

AI-written and checked against the verified answer.

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