# Binomial Coefficient/Examples/5 from 2

## Example of Binomial Coefficient

$\dbinom 2 5 = 0$

## Proof

From the definition of binomial coefficient:

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

Here we have $k = 5$ and $n = 2$.

As $k > n$:

$\dbinom 2 5 = 0$

$\blacksquare$