Probability & Statistics

Permutation Calculator

Calculate the exact number of possible ways you can arrange datasets. Input your Total Items (n) and the Amount Chosen (r) to simultaneously calculate both Permutations (nPr) and Combinations (nCr).

Last updated: February 24, 2026

Displays Permutations (where order matters) and Combinations concurrently
Easily toggles Replacement logic (with vs. without repetition)
Utilizes BigInt caching architecture to prevent 'Infinity' crashes on large factorial sets

Are you actually calculating combinations of identical outcomes over time? Try the Binomial Calculator

Permutation Calculator
Computed
Calculate total ways to arrange datasets choosing r items from n options.

Experiment Parameters

Can an item be picked more than once?

Results

Permutations

Order Matters
720Formula: P(n,r) = n! / (n-r)!

Combinations

Order Ignores
120Formula: C(n,r) = n! / [r!(n-r)!]

Understanding The Math

Permutations (Order Matters)

Permutations define all unique ordered sequences. Because the order of elements is strictly enforced, choosing the items A-B-C is counted as entirely distinct from C-B-A.

Without Repetition: P(n,r) = n! / (n-r)!
With Repetition: n^r

Combinations (Order Doesn't Matter)

Combinations define group selections where the sequence is irrelevant. Here, choosing A-B-C is considered the exact same group as C-B-A. Because of this structural reduction, Combinations are always drastically smaller than Permutations.

Without Repetition: C(n,r) = n! / (r! * (n-r)!)
With Repetition: C(n+r-1, r)

Frequently Asked Questions

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Permutation Calculator - Combinations & Arrangements (nPr, nCr)