basic

Permutations and Combinations Calculator

P(n,r) = n!/(n−r)!; C(n,r) = n!/(r!(n−r)!).

Calculates nPr = n!/(n−r)! (ordered arrangements) and nCr = n!/(r!(n−r)!) (unordered selections) for given n and r. Also shows the ratio nPr/nCr = r!.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

nPr = n!/(n−r)!; nCr = n!/(r!(n−r)!)

In depth

Calculates nPr = n!/(n−r)! (ordered arrangements) and nCr = n!/(r!(n−r)!) (unordered selections) for given n and r. Also shows the ratio nPr/nCr = r!.