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