Definition:Binomial Coefficient

Let $$m, n \in \N$$.

Then the symbol $$\binom n m$$ is interpreted as:



\binom n m = \begin{cases} \displaystyle \frac {n!} {m! \left({n - m}\right)!} & : m \le n \\ 0 & : m > n \end{cases} $$

The number $$\binom n m$$ is known as a binomial coefficient.

See the Binomial Theorem for the reason why.

$$\binom n m$$ is read n choose m.