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Chapter 11: Problem 33

In Exercises 33-40, use the formula for \({ }_{n} P_{r}\) to evaluate each expression. \({ }_{9} P_{4}\)

Short Answer

Expert verified
\({ }_{9} P_{4}\) equals 15120.

Step by step solution

01

Identify the values of n and r

In the permutation formula \({ }_{n} P_{r}\), n represents the total number of items you have, and r stands for the number of items you select at a time. From the given question \({ }_{9} P_{4}\), the value of 'n' is 9 and 'r' is 4.
02

Find Factorials

Find the factorial of n (\(9!\)) and n-r (\((9-4)!\)), which is \(5!\). The factorial of a number is the product of all positive integers less than or equal to that number. The factorial of 9, denoted \(9!\), is \(9*8*7*6*5*4*3*2*1\), and the factorial of 5, denoted \(5!\), is \(5*4*3*2*1\).
03

Apply the Permutation Formula

The permutation formula \({ }_{n} P_{r}\) = \(n! / (n-r)!\). In our case, this would look like: \({ }_{9} P_{4}\) = \(9! / 5!\). Perform the division to finalize your answer.

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