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Probability · Counting

Permutations & Combinations Calculator

Count permutations, arrangements, and combinations with or without repetition while making the roles of order, selection size, and constraints explicit.

Formula shown Runs locally Reviewed Aug 11, 2026
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Equation guide

Finite selections where order and repetition are explicitly chosen

Permutations

n!

Without repetition

P(n,r)=n!/(n−r)!C(n,r)=n!/[r!(n−r)!]

With repetition

Ordered: nʳUnordered: C(n+r−1,r)=(n+r−1)!/[r!(n−1)!]
Counting methods

Count ordered and unordered selections

Inputs and displayed decimal results use at most three decimal places. Exact internal values are retained during calculation.

n!/[r!(n−r)!]

Choose whether order and repetition matter, then enter n and r.

Using the model

Symbols, assumptions and limitations

Interpretation notes

Inputs n and r are non-negative integers. Without repetition, r cannot exceed n. Exact integer arithmetic is used up to the documented input limit, so large results are not rounded.

Worked examples

See the method in practice

01

Choose a committee

Choosing 2 people from 5 without regard to order gives C(5,2) = 10.

02

Assign two ordered roles

Selecting a president and secretary from 5 people gives P(5,2) = 20 because order matters.

Questions

Frequently asked

When does order matter?

Order matters when changing positions creates a different outcome, such as assigning distinct roles.

What does repetition mean?

Repetition allows the same available type or symbol to be chosen more than once.

Why are results not rounded?

Counting results are exact whole numbers, so the calculator uses integer arithmetic rather than decimal approximation.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

OpenStax Introductory Statistics — Counting Rules

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology