Definition:Binomial Coefficient/Integers/Definition 2

Definition
Let $n \in \Z_{\ge 0}$ and $k \in \Z$.

The number of different ways $k$ objects can be chosen (irrespective of order) from a set of $n$ objects is denoted:
 * $\dbinom n k$

This number $\dbinom n k$ is known as a binomial coefficient.

Also see

 * Equivalence of Definitions of Binomial Coefficient
 * Cardinality of Set of Subsets