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Chapter 11: Problem 64

I used the formula for \({ }_{n} P_{r}\) to determine the number of ways the manager of a baseball team can form a 9-player batting order from a team of 25 players.

Short Answer

Expert verified
The number of ways to form a unique 9-player batting order from a team of 25 players is \({ }_{25} P_{9} = 25! / (25-9)!\).

Step by step solution

01

Identify the Variables

Here, the total number of players, i.e. 'n', is 25 and the number of players to choose for the batting order, or 'r', is 9.
02

Apply the Permutation Formula

Now, plug the values of 'n' and 'r' into the permutation formula. This means calculate the factorial of 25 (\(25!\)), divide it by the factorial of the difference between 25 and 9 (\((25-9)!\)).
03

Calculate the Result

Perform the division operation to get the number of different ways the 9-player batting order can be arranged from a team of 25 players.

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