# Permutation and Combination Calculator

> Calculate exact permutations and combinations with or without replacement.

Page: https://askcalculators.com/calculator/permutation-and-combination-calculator/
Definition: https://askcalculators.com/calculator/permutation-and-combination-calculator/definition.json
JSON Schema: https://askcalculators.com/calculator/permutation-and-combination-calculator/schema.json
Version: 1.0.0
Maintained by: AskCalculators (software project; not a credentialed reviewer)
Qualified review: pending. Automated checks do not establish professional approval.
Page status: Live
Review status: Pending

## Use
Open the calculator page and enter values. Query-string parameters can restore and bookmark a calculation.
Example: https://askcalculators.com/calculator/permutation-and-combination-calculator/?totalItems=6&selectedItems=2&replacement=without

## Inputs
- totalItems: Total amount in the set (n); type=number; required; default=6; min=0; max=500
- selectedItems: Amount in each subset (r); type=number; required; default=2; min=0; max=500
- replacement: Selection rule; type=select; required; default=without; values=without|with

## Outputs
- permutations: Permutations; format=text; primary
- combinations: Combinations; format=text
- permutationFormula: Permutation formula; format=text
- combinationFormula: Combination formula; format=text

## Formula
Without replacement: nPᵣ=n!/(n−r)! and nCᵣ=n!/[r!(n−r)!]; with replacement: nʳ and C(n+r−1,r).

## Rules
- Empty optional inputs are undefined, not zero.
- Hidden conditional inputs are ignored.
- Do not invent missing required inputs.