Binomial Coefficient

In mathematics, the binomial coefficients are positive integers that occur as coefficients in the binomial theorem.

Commonly, a binomial coefficient is indexed by a pair of integers $n\ge k\ge 0$ and is written $\left(\genfrac{}{}{0ex}{}{n}{k}\right)$. It is the coefficient of the $x^k$ term in the polynomial expansion of the binomial power $(1+x{)}^n$

It can also be interpreted as the number of ways to choose $k$ elements from a set of $n$ elements without regard to the order of selection. This is also known as “n choose k”.

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