---
title: "Permutation & Combination Calculator — nPr and nCr with Steps"
description: "Calculate nPr (permutations) and nCr (combinations) instantly. Shows step-by-step factorial calculation. Covers US C(n,r), UK ⁿCᵣ, and IB notation. Exact results for n up to 170."
url: "https://worldcalculators.org/calculators/permutation-combination/"
canonical: "https://worldcalculators.org/calculators/permutation-combination/"
---

# Permutation & Combination Calculator

Calculate nPr (permutations) and nCr (combinations) instantly. Shows step-by-step factorial calculation. Covers US C(n,r), UK ⁿCᵣ, and IB notation. Exact results for n up to 170.

## Quick answer

Ask: "Does the order matter?" If yes → permutation. If no → combination. Examples: Passwords (order matters) → permutation. Lottery numbers (which numbers you pick, not order) → combination. Ranking candidates (1st, 2nd, 3rd) → permutation. Choosing a committee → combination. Seating arrangements → permutation. Choosing pizza toppings → combination.

## Frequently Asked Questions

Ask: "Does the order matter?" If yes → permutation. If no → combination. Examples: Passwords (order matters) → permutation. Lottery numbers (which numbers you pick, not order) → combination. Ranking candidates (1st, 2nd, 3rd) → permutation. Choosing a committee → combination. Seating arrangements → permutation. Choosing pizza toppings → combination.
Both notations mean exactly the same thing — it's purely a typographic convention adopted by different education systems. UK Edexcel and AQA exam boards use ⁿCᵣ (superscript-subscript format) on their formula sheets. US textbooks and AP Statistics use C(n,r) or the horizontal notation nCr. IB Mathematics uses both interchangeably. In computing (Python, Excel), it's written as comb(n, r) or COMBIN(n, r).

Source: https://worldcalculators.org/calculators/permutation-combination/
Markdown mirror of the HTML page. Prefer this URL for RAG; the interactive calculator still lives on the HTML page.