Use the formula for $$ { }_{n} P_{r} $$ to evaluate the following expression. $$ { }_{5} P_{5} $$ $$ { }_{5} P_{5}=\square $$

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To evaluate the expression $$ { }_{5} P_{5} $$, we can use the formula for permutations:

$$ { }_{n} P_{r} = \frac{n!}{(n-r)!} $$

In this case, $$ n = 5 $$ and $$ r = 5 $$, so we substitute these values into the formula:

$$ { }_{5} P_{5} = \frac{5!}{(5-5)!} $$

Now, we can calculate the factorial of 5 and the factorial of 0, and then simplify the expression to find the value of $$ { }_{5} P_{5} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{5!}{\left(5-5\right)!}$$
- step1: Subtract the terms:
  $$\frac{5!}{0!}$$
- step2: Reduce the fraction:
  $$5!$$
- step3: Calculate:
  $$120$$
$$ { }_{5} P_{5} = 120 $$

Use the formula for \( { }_{n} P_{r} \) to evaluate the following expression. \( { }_{5} P_{5} \) \( { }_{5} P_{5}=\square \)

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