---
type: "problem"
title: "Binomial coefficient identity with a bijection"
slug: "binomial-coefficient-identity-with-a-bijection"
author: "ancient-tree"
tags: ["bijection", "binomial coefficients"]
difficulty: 35
qualityStatus: "unreviewed"
listed: true
origin: "Unknown"
originChapter: ""
originPage: ""
originNote: ""
license: "CC BY-SA 4.0"
---

Let $n$ be a positive integer and $1\leq k \leq n$. Show with a bijection that : $$k\binom{n}{k}=n\binom{n-1}{k-1}$$