Permutations & Combinations Calculator

Exact nPr, nCr and factorials for large numbers, with and without repetition, using big-integer arithmetic.

Your result will appear here

Fill in the fields and press Calculate, or pick one of the examples.

About the Permutations & Combinations Calculator

Counts the ways to choose r items from n, in every variant: ordered or unordered, with or without repetition, plus n!. All results are exact integers computed with big-integer arithmetic, so 100! and C(1000, 500) are given in full rather than as rounded floating-point values.

Limitations

n and r are limited to 10,000 (5,000 for combinations with repetition). Very long results are abbreviated on screen; Copy gives every digit.

How to use it

Enter n (items available) and r (items chosen).
Press Calculate.
Pick the result that matches your problem: does order matter, and can items repeat?

Example

n = 5, r = 2

→ P(5, 2) = 20, C(5, 2) = 10

Formulas used

P(n, r) = \frac{n!}{(n - r)!}

Permutations: order matters, no repetition.

C(n, r) = \binom{n}{r} = \frac{n!}{r!\,(n - r)!}

Combinations: order does not matter, no repetition.

n^{r},\qquad \binom{n + r - 1}{r}

With repetition: ordered and unordered selections.

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About the Permutations & Combinations Calculator

Limitations

How to use it

Formulas used

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About the Permutations & Combinations Calculator

Limitations

How to use it

Formulas used