# Combination and Permutation Calculator - C(n,r), P(n,r) and n!

> Free online combination and permutation calculator: exact C(n,r), P(n,r) and n! with big integers, plus repetition variants and the total number of subsets.

- URL: https://qilingtools.com/en/math/combination
- Category: Math Tools (https://qilingtools.com/en/math)
- Tags: [Math](https://qilingtools.com/en/tags/math), [Statistics](https://qilingtools.com/en/tags/statistics)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Compute C(n,r), P(n,r) and n! without running out of digits: results are exact big integers, shown in full alongside scientific notation, with combinations with repetition and the total number of subsets included.

## How to use

1. Choose combinations, permutations or factorial
2. Enter n and r
3. Read the exact value, or copy the scientific-notation form for very long results

## Features

- Exact big-integer arithmetic, no lost digits
- Combinations, permutations and factorials together
- Includes C(n+r-1,r), nʳ and 2ⁿ
- Formula plus a plain-language reading of the result

## FAQ

### What is the difference between a permutation and a combination?

Combinations ignore order (which items you pick), permutations count order too. They are related by P(n,r) = C(n,r) × r!.

### How is C(n,r) computed?

C(n,r) = n! / (r! × (n-r)!), evaluated as a running product with cancellation so intermediate values never blow up.

### How large can n be?

Up to 1000 for combinations and permutations and 2000 for factorials, all computed exactly.

### What is 0! ?

It is 1 by definition, which keeps identities such as C(n,0)=1 consistent.

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