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Chapter 11: Problem 35

Use the formula for \({ }_{n} P_{r}\) to evaluate each expression. \({ }_{8} P_{5}\)

Short Answer

Expert verified
The value of \( _8P_5 \) is 6720.

Step by step solution

01

Identify n and r

In this permutation symbol \( _8P_5 \), we have 8 as 'n' (total number of items) and 5 as 'r' (number of items we are selecting and arranging).
02

Plug values into permutation formula

Now that we have identified n and r, we can substitute them into the permutation formula \( _nP_r = \frac{n!}{(n-r)!} \). This gives us \( _8P_5 = \frac{8!}{(8-5)!} \).
03

Compute Factorials and Solve

First, we need to compute the factorials. 8! = 8*7*6*5*4*3*2*1 = 40320 and (8-5)! = 3! = 3*2*1 = 6. Now, we substitute these into the equation and we get \( _8P_5 = \frac{40320}{6} = 6720. \)

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