How it works
Calculate exact permutations and combinations with or without replacement. Inputs are calculated locally in the browser, and valid values are retained in the page URL for bookmarking.
Input query strings and outputs
Use an input name in this page’s URL as ?name=value, and join additional inputs with &. Portable shared links may instead use the compact ?ac= state parameter.
Input query strings
3-
?totalItems=Total amount in the set (n)Number · Required · Default: 6
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?selectedItems=Amount in each subset (r)Number · Required · Default: 2
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?replacement=Selection ruleChoice · Required · Default: without · Accepted values: without, with
Outputs
4-
permutationsPermutationsText · Primary output
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combinationsCombinationsText
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permutationFormulaPermutation formulaText
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combinationFormulaCombination formulaText
Formula notes
Without replacement: nPᵣ=n!/(n−r)! and nCᵣ=n!/[r!(n−r)!]; with replacement: nʳ and C(n+r−1,r).
Input guidance
Use consistent units for every length or measurement in the same calculation. Results are educational mathematical estimates and should be checked before high-stakes use.