When do I use permutations vs combinations?

Use permutations (nPr) when order matters, like race finishes or PINs. Use combinations (nCr) when order doesn't, like lottery numbers or committee picks.

Why do big numbers show as 'too large'?

Factorials grow extremely fast; beyond 170! the result exceeds what standard numbers can represent.

Permutation & Combination Calculator

Calculate nPr, nCr and factorials — ordered and unordered selections from n items.

n (total items)r (chosen)

Permutations nPr

720

Combinations nCr

120

Factorial n!

3,628,800

Permutations count ordered selections (nPr = n!/(n−r)!); combinations count unordered ones (nCr = n!/(r!(n−r)!)).

What Is the Permutation & Combination Calculator?

The Permutation & Combination Calculator computes nPr (ordered arrangements), nCr (unordered selections, the binomial coefficient) and the factorial n! from your values of n and r. It's the go-to tool for counting problems in probability, statistics and combinatorics.

How It Works

Enter n (total items) and r (how many are chosen). Permutations, combinations and n! update instantly.

When to Use It

For probability and statistics homework, lottery-odds and poker-hand counting, and any combinatorics problem where order does or doesn't matter.

Frequently Asked Questions

When do I use permutations vs combinations?: Use permutations (nPr) when order matters, like race finishes or PINs. Use combinations (nCr) when order doesn't, like lottery numbers or committee picks.
Why do big numbers show as 'too large'?: Factorials grow extremely fast; beyond 170! the result exceeds what standard numbers can represent.

Last reviewed: 2026-06-27

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