Chapter 12.6, Problem 20PPE

To determine

To calculate: The value of expression $P{}_5$ .

Answer to Problem 20PPE

The value is $120$ .

Explanation of Solution

Given information:

  $P{}_5$

Formula used:

A permutation is an arrangement of objects in a specific order. The expression $P{}_r$ represents the number of permutations of $n$ objects arranged $r$ at a time.

  $P{}_r=\frac{n!}{\left(n-r\right)!}$

For any positive integer $n$, the expression $n$ factorial is written as $n!$ and is the product of integers from n down to 1.

Calculation:

Consider ,

  $P{}_5$

  $\begin{array}{l}P{}_5=\frac{5!}{\left(5-5\right)!}\\ =\frac{5!}{0!}\\ =\frac{5!}{1}\\ =5\times 4\times 3\times 2\times 1\\ =120\end{array}$

Hence, the value is $120$ .