Question
Evaluate the expression \( { }_{5} \mathrm{P}_{5} \) \( { }_{5} \mathrm{P}_{5}=\square \)
Ask by Knight Wheeler. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( { }_{5} \mathrm{P}_{5} = 120 \)
Solution
Calculate or simplify the expression \( 5! \).
Simplify the expression by following steps:
- step0: Solution:
\(5!\)
- step1: Calculate:
\(120\)
The value of \( { }_{5} \mathrm{P}_{5} \) is 120.
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Simplify this solution Mind Expander
The expression \( { }_{5} \mathrm{P}_{5} \) represents the number of permutations of 5 items taken 5 at a time, which means we're arranging all 5 items. The formula for permutations is given by: \[ _{n}P_{r} = \frac{n!}{(n-r)!} \] In this case, \( n = 5 \) and \( r = 5 \): \[ _{5}P_{5} = \frac{5!}{(5-5)!} = \frac{5!}{0!} = \frac{5!}{1} = 5! = 120 \] Thus, \( { }_{5} \mathrm{P}_{5} = 120 \).
