Permutation and Combination Calculator

Calculate nPr and nCr, with and without repetition, exactly — even for very large numbers.

Result

Enter your values and select Calculate to see the result.

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How the Permutation and Combination Calculator works

Enter the total number of items n and how many you choose, r. A permutation counts arrangements where order matters (1st, 2nd and 3rd place); a combination counts selections where it doesn't (a team of three). The calculator also covers choosing with repetition, and every result is an exact whole number, however large.

Formulas

Permutations

P(n, r) = n! ÷ (n − r)!

Combinations

C(n, r) = n! ÷ (r! (n − r)!)

With repetition

n^r arrangements; C(n + r − 1, r) selections

Examples

Podium places for 10 runners

P(10, 3) = 720 ways to award gold, silver and bronze; C(10, 3) = 120 ways to pick three runners.

A 6-from-49 lottery

C(49, 6) = 13,983,816 possible tickets.

Frequently asked questions

When does order matter?

When swapping two chosen items gives a different outcome — rankings, codes and seating orders.

What does 'with repetition' mean?

An item can be chosen more than once, like digits in a PIN: 10³ = 1,000 three-digit codes.

Why is C(n, r) = 0 when r > n?

You can't pick more different items than exist.

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