## Precalculus (6th Edition) Blitzer

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