Menu
Formula verified · Deterministic calculation

Permutation Calculator

Enter the total number of distinct objects and the number selected to calculate permutations without replacement.

Permutations60
Total objects (n)5
Selected objects (r)3
CalcuMint Pro

Advanced Analysis

Compare plans
Advanced chartsExplore the result across time and assumptions.
Scenario comparisonCompare multiple assumptions side by side.
Sensitivity analysisSee which assumptions change the outcome most.
Goal SolverSolve backwards from the outcome you want.
Result methodology

Exact ordered selections without replacement using P(n,r)=n!/(n−r)!.

Solution steps
  1. n = 5; r = 3
  2. P(n,r) = n!/(n-r)! = 60

How this calculator works

Permutations use P(n,r)=n!/(n−r)! and count arrangements where order matters.

Formula

P(n,r)=n!/(n−r)!

Counts ordered selections of r objects from n distinct objects without replacement.

Worked example

Five choose three in order is a verified test case used by the calculation engine.

Assumptions and limitations

  • n and r are non-negative integers with r≤n.
  • Objects are distinct and selections are made without replacement.
  • Results are limited to the supported exact integer range.

Methodology & sources

This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint.

  • CalcuMint deterministic statistics engine

Frequently asked questions

When should I use permutations instead of combinations?

Use permutations when the order of selected objects matters.

What is P(n,0)?

There is one ordered selection of zero objects, so P(n,0)=1.

Related calculators

Probability CalculatorCombine two event probabilities under an explicit independence assumption.Combination CalculatorCalculate unordered selections of r objects from n distinct objects.Mean Median Mode Range CalculatorCalculate mean, median, mode, minimum, maximum and range from a dataset.