## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 10 - Section 10.6 - Counting Principles, Permutations, and Combinations - Concept and Vocabulary Check - Page 1103: 3

#### Answer

The number of possible permutations if $r$ objects are taken from $n$ items is $_{n}{{P}_{r}}=$ $\frac{n!}{\left( n-r \right)!}$

#### Work Step by Step

The permutations of $n$ things taken $r$ at a time can be defined by the formula: ${}_{n}{{P}_{r}}=\frac{n!}{\left( n-r \right)!}$ Let us take an example: The permutation of 5 things taken 3 at a time is defined by: $_{5}{{P}_{3}}=\frac{5!}{\left( 5-3 \right)!}$ Thus, the number of possible permutations if $r$ objects are taken from $n$ items is $_{n}{{P}_{r}}=$ $\frac{n!}{\left( n-r \right)!}$

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