---
type: "problem"
title: "Probability of commuting in a finite group"
slug: "probability-of-commuting-in-a-finite-group"
author: "sequoia"
tags: ["finite group", "probability"]
difficulty: 69
qualityStatus: "unreviewed"
listed: true
origin: "Unknown"
originChapter: ""
originPage: ""
originNote: ""
license: "CC BY-SA 4.0"
---

Let $G$ be a finite group that is not abelian.

Show that the probability of picking randomly two commuting elements of the group is less or equal than $\frac58$.