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Chapter 11: Problem 66

I used the formula for \({ }_{n} P_{r}\) to determine the number of ways people can select their 9 favorite baseball players from a team of 25 players.

Short Answer

Expert verified
The number of ways people can select their 9 favorite baseball players from a team of 25 players is given by \({ }_{25} P_{9} = \frac{25!}{(25-9)!}\).

Step by step solution

01

Identify `n` and `r` in the permutation formula

`n` represents the number of items to choose from. In this case, n is the number of baseball players, which is 25. `r` represents how many items are being chosen, which in this scenario is 9.
02

Apply the permutation formula

Now that we have identified `n` as 25 and `r` as 9, the puzzle can be solved by applying these values to the permutation formula: \({ }_{25} P_{9} = \frac{25!}{(25-9)!}\).
03

Solve the factorial notation and compute

Now, evaluate 25! and (25-9)! and then perform the division. The result will give the number of ways 9 baseball players can be selected from a team of 25.

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