combination

combinatorics

what

The number of different ways to choose $k$ objects from $n$ objects.

symbol

$${}^n{C}_k$$

or

$$\left(\genfrac{}{}{0ex}{}{n}{k}\right)$$

formula

$$\begin{array}{rl}\left(\genfrac{}{}{0ex}{}{n}{k}\right)={}^n{C}_k& =\frac{n!}{k!(n-k)!}\\ & \\ & =\frac{{}^n{P}_k}{k!}\end{array}$$

where $\text{Perm}nk$ is the permutation.