Question
Use the formula for \( { }_{n} P_{r} \) to evaluate the following expression. \( { }_{5} P_{5} \) \( { }_{5} P_{5}=\square \)
Ask by Welch Pearson. in the United States
Mar 18,2025
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Answer
\( { }_{5} P_{5} = 120 \)
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To evaluate \( { }_{5} P_{5} \), we can use the permutation formula \( { }_{n} P_{r} = \frac{n!}{(n-r)!} \). In this case, since both \( n \) and \( r \) are equal to 5, the formula simplifies to: \[ { }_{5} P_{5} = \frac{5!}{(5-5)!} = \frac{5!}{0!} \] We know that \( 0! = 1 \) and \( 5! = 120 \), so: \[ { }_{5} P_{5} = \frac{120}{1} = 120 \] Thus, \( { }_{5} P_{5} = 120 \).