Permutations & Combinations

Count arrangements and selections with nPr, nCr and factorials, showing when order matters. Try “how many ways to choose 3 from 10?”.

Try an example:

What you can do with the Permutations & Combinations

Counting arrangements and selections, factorials.

Enter your values or describe the problem in the calculator above. Review the result and the explanation before using it in homework, study or practical calculations.

Example input

e.g. how many ways to choose 3 from 10?

How the Permutations & Combinations works

  1. Decide whether order matters: yes for permutations, no for combinations.
  2. Use nPr = n! ÷ (n − r)! or nCr = n! ÷ (r!(n − r)!).
  3. Cancel the factorials and calculate (10C3 = 120).

Frequently asked questions

What is the difference between a permutation and a combination?

A permutation counts ordered arrangements; a combination counts unordered selections.

What is 0!?

By definition, 0! = 1.

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