Chapter 13.2, Problem 5AYU

$P\left(n,r\right)=$ __________________.

To determine

To fill: $P(n,r)=$ _____

Answer to Problem 5AYU

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

Explanation of Solution

Given:

$P(n,r)$

Calculation:

$P(n,r)$ is the permutation of $r$ objects chosen from $n$ Distinct objects without repetition.

Permutations of $r$ objects Chosen from $n$ Distinct Objects without Repetition

The number of arrangements of $n$ objects using $r\le n$ of them, in which

1. The $n$ objects are distinct,

2. Once an object is used it cannot be repeated, and

3. Order is important,

is given by the formula

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