Permutation & Combination Calculator

Calculate permutations (nPr) and combinations (nCr) for choosing r items from n, with the factorial behind each. Calculates in your browser.

Use whole numbers with r no larger than n.

Permutations (nPr)

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Combinations (nCr)-

Show the math

Permutations count ordered arrangements; combinations count unordered selections:

nPr = n! ÷ (n − r)!

nCr = n! ÷ (r! × (n − r)!)

Use a permutation when order matters (1st, 2nd, 3rd on a podium) and a combination when it does not (a hand of cards). r cannot exceed n. All math runs locally in your browser.

What this does

This calculator finds the number of permutations (nPr) and combinations (nCr) when choosing r items from a set of n. Permutations count arrangements where order matters; combinations count selections where it does not.

How to use it

  1. Enter the total number of items, n.
  2. Enter how many you are choosing, r.
  3. Read both the permutations and the combinations.

How it works

Permutations divide n factorial by (n − r) factorial. Combinations divide that again by r factorial, because each unordered selection has r! orderings. Both require r ≤ n.

nPr = n! ÷ (n − r)!; nCr = n! ÷ (r! × (n − r)!)

Understanding your result

Use permutations when the order of the chosen items matters — a podium of 1st, 2nd, 3rd — and combinations when it does not, like a hand of cards or a committee. Permutations are always the larger of the two, by exactly a factor of r!, since every unordered group can be arranged r! ways.

Example

Choosing 3 from 5: there are 60 permutations (5P3) but only 10 combinations (5C3).

Sources & methodology

Last updated .

Frequently asked questions

What is the difference between a permutation and a combination?

A permutation counts arrangements where order matters; a combination counts selections where order does not. nPr is always larger than nCr by a factor of r!.

When should I use each one?

Use permutations for ordered outcomes — race finishes, passwords, seat orders. Use combinations for unordered groups — lottery numbers, card hands, committees.

What if r is bigger than n?

You cannot choose more items than exist, so both nPr and nCr are undefined when r is greater than n.

Is my data stored?

No. Everything is calculated locally in your browser.