Answer
The number of possible combinations if $r$ objects are taken from $n$ items is
$_{n}{{C}_{r}}=$ $\frac{n!}{r!\left( n-r \right)!}$.
Work Step by Step
We know that the combinations of $n$ things taken $r$ at a time can be defined by the formula:
${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$
Let us take an example:
The combination of 5 things taken 3 at a time is provided by:
${}_{5}{{C}_{3}}=\frac{5!}{3!\left( 5-3 \right)!}$
Thus, the number of possible combinations if $r$ objects are taken from $n$ items is
$_{n}{{C}_{r}}=$ $\frac{n!}{r!\left( n-r \right)!}$.
