Permutation and Combination Calculator

Enter n (items to choose from) and r (items chosen).

Result

Enter values and press Calculate to see the result.

Formula

nPr=n!(n−r)!{}_nP_r = \frac{n!}{(n - r)!}

Permutations: order matters.

nCr=n!r! (n−r)!{}_nC_r = \frac{n!}{r!\,(n - r)!}

Combinations: order does not matter.

How to use this calculator

  1. Enter whole numbers with r no bigger than n.
  2. Press Calculate to get both counts.

Worked example

Choose 2 from 5

5P2 = 5 × 4 = 20 ordered arrangements.

5C2 = 20 / 2! = 10 unordered selections.

Frequently asked questions

When does order matter?

For rankings or codes (permutations). For teams or hands of cards, order doesn’t matter (combinations).

Are the answers exact?

Yes — even very large counts are computed exactly.