Calculate nPr and nCr

Count ordered permutations and unordered combinations from n items choosing r.

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ToolPermutation & Combination
Input
Output
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How it works

Permutations use n! ÷ (n−r)!, while combinations divide that result by r! to ignore order. Inputs must be integers with 0 ≤ r ≤ n and fit bounded factorial arithmetic.

  • Both counts appear because order determines the formula.
  • The factorial limit is 170.

Worked example

Lottery Combinations
Calculate combinations for choosing 6 from 49
Input
											49, 6
Output
												n = 49, r = 6
P(49, 6) = 10068347520
C(49, 6) = 13983816

When to use this

Committee counts use combinations, password exercises use ordered selections, and card lessons contrast the two counts.

Edge cases

  • r greater than n is rejected without replacement.
  • n = 0 and r = 0 produce one empty selection.
  • Large factorial operands are limited before overflow.