$$\begin{array}{rcl}\text{f}\left(k;n,p\right)& =& {}_n{C}_k{p}^k{\left(1-p\right)}^{n-k}\\ & =& \frac{n!}{k!\left(n-k\right)!}{p}^k{\left(1-p\right)}^{n-k}\end{array}$$