Math & Statistics

Permutation & Combination Calculator

Calculate nPr (permutations) and nCr (combinations).

Enter n (total items) and r (items chosen) to calculate the number of permutations (order matters) and combinations (order doesn't matter).

Enter a valid whole number.
r cannot be greater than n.

Permutations (nPr)

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Combinations (nCr)

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How to Use This Tool

  1. Enter n, the total number of items.
  2. Enter r, the number of items being chosen or arranged.
  3. Click Calculate for both permutation and combination counts.

Permutation vs. Combination

Permutation (Order Matters)

nPr = n! ÷ (n−r)!

Use permutations when the order of selection matters — like arranging 3 people in a line from a group of 10, where who's first, second, and third all matter.

Combination (Order Doesn't Matter)

nCr = n! ÷ [r! × (n−r)!]

Use combinations when only the group selected matters, not the order — like choosing 3 people from 10 for a committee, where it doesn't matter who was "picked first."

Why Combinations Are Always Smaller

Combinations equal permutations divided by r! (the number of ways to arrange the r chosen items), since each unique combination corresponds to multiple different-ordered permutations — this is why nCr is always less than or equal to nPr.

Frequently Asked Questions

How do I know whether to use permutation or combination?

Ask whether order matters for your problem. If arranging items in different orders creates different outcomes (like a race's 1st/2nd/3rd place), use permutation. If only the group selected matters (like choosing team members), use combination.

What is the maximum n this calculator supports?

This calculator supports n up to 170, beyond which factorial values exceed JavaScript's maximum safe number precision.

This calculator is provided for general informational and estimation purposes only. Results should not be treated as professional financial, tax, legal, medical, or engineering advice. Always verify critical calculations with a qualified professional or official source before making decisions.