Permutation vs Combination
Permutation vs combination compared — whether order matters, formulas and examples, with a free combinatorics calculator.
A permutation counts arrangements where order matters; a combination counts selections where it does not. The only difference is whether ABC and ACB count as the same.
Permutation vs Combination at a glance
| Permutation | Combination | |
|---|---|---|
| Order matters? | Yes | No |
| Formula | nPr = n! / (n−r)! | nCr = n! / (r!(n−r)!) |
| Example | Race finishing order | Picking a committee |
When to use Permutation
Use a permutation when arrangement matters — rankings, passwords, sequences.
When to use Combination
Use a combination when only the group matters, not its order — lottery draws, teams.
Tools for Permutation & Combination
Combinations & Permutations Calculator
Exact nCr, nPr and n! with big-integer precision. Client-side, no signup.
Open toolProbability Calculator
Single events, independent AND/OR, and the binomial distribution P(X=k)/P(X≤k)/P(X≥k). Client-side.
Open toolStatistics Calculator
Descriptive statistics — mean, median, mode, range, variance, SD, quartiles (sample & population). Client-side; data never leaves your device.
Open toolScientific Calculator
Online scientific calculator — trig, log, powers, roots, factorial, π/e, DEG/RAD, with a proper expression parser. Client-side.
Open toolPermutation vs Combination
How do I know whether to use a permutation or combination?
Ask whether order matters. If rearranging the same items counts as a different outcome (a ranking, a sequence), use a permutation. If not (a group, a selection), use a combination.