Binomial coefficient
= Binomial coefficient
{title2=$\binom{n}{k}$}
{wiki}
The <binomial coefficient>
$$
\binom nk=\frac{n!}{k!(n-k)!}
$$
counts the $k$-element subsets of an $n$-element set. Equivalently, it counts strings containing $k$ copies of one symbol and $n-k$ copies of another.