Binomial coefficient calculator

The binomial coefficient counts the number of k-element combinations of n items. It is written as $(\genfrac{}{}{0ex}{}{n}{k})$, and the formula for it is

$$(\genfrac{}{}{0ex}{}{n}{k})=\frac{n!}{(n-k)!\cdot k!}$$

For example, if we have six letters {a, b, c, d, e, f} and want to know how many groups of three letters we can make from them, we write it as $(\genfrac{}{}{0ex}{}{6}{3})=20$. You can find more about the binomial coefficient in the article on combinations. Enter the values of n and k into the calculator below and you will see the result straight away.