Category:Definitions/Binomial Coefficients

This category contains definitions related to Binomial Coefficients.
Related results can be found in Category:Binomial Coefficients.

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

Then the binomial coefficient $\dbinom n k$ is defined as:

$\dbinom n k = \begin{cases} \dfrac {n!} {k! \paren {n - k}!} & : 0 \le k \le n \\ & \\ 0 & : \text { otherwise } \end{cases}$

where $n!$ denotes the factorial of $n$.