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Chapter 11: Problem 39

Use the formula for \({ }_{n} P_{r}\) to evaluate each expression. \({ }_{8} P_{0}\)

Short Answer

Expert verified
The value of \({ }_{8} P_{0}\) is 1.

Step by step solution

01

Understanding Permutation

The formula for permutation \({ }_{n} P_{r}\) represents the number of ways 'r' elements can be chosen from a total of 'n' elements, considering the order of arrangement. It is calculated as \({ }_{n} P_{r} = \frac{n!}{(n-r)!}\), where '!' denotes factorial.
02

Applying the Permutation Formula

We apply this formula to \({ }_{8} P_{0}\). Here, 'n' is 8 and 'r' is 0. Substituting these values into the permutation formula gives: \({ }_{8} P_{0} = \frac{8!}{(8-0)!}\).
03

Calculating the Value

Solving the above equation: \({ }_{8} P_{0} = \frac{8!}{8!}\). By the property of fractions, when the numerator and denominator are equal, the fraction equates to 1. Therefore, the value of \({ }_{8} P_{0} = 1\).

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