---
type: "concept"
title: "Binomial coefficient"
slug: "binomial-coefficient"
language: "en"
translationGroupId: "cmrcfvzfn000ls7011xplay6g"
domain: "Number theory"
status: "stub"
aliases: []
lastEditedBy: "ancient-tree"
---

The binomial coefficient, $\binom{n}{k}$, read $k$ among $n$, is the number of [[Subset|subsets]] of [[Cardinal|cardinal]] $k$ of a set with $n$ elements. It is equal to:
$$\binom{n}{k}=\frac{n!}{k!(n-k)!}$$
##### Proof