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Calculate P(n,r) and C(n,r) with step-by-step formulas.
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Permutation-Combination Calculator computes nPr (permutations) and nCr (combinations) from n total items and r chosen, the core counting tools of probability and statistics.
The whole distinction comes down to one question: does order matter? Permutations count arrangements where it does (a race podium, a password, a sequence), while combinations count selections where it doesn't (a committee, a hand of cards, a group). Asking 'if I rearrange the chosen items, is it a different outcome?' resolves almost every permutation-vs-combination problem.
Mathematically, nPr = n! ÷ (n−r)! and nCr = n! ÷ (r!(n−r)!), the only difference being that combinations divide by an extra r! to strip out the duplicate orderings permutations count separately. That's why nCr is always less than or equal to nPr for the same inputs.
Because these use factorials, the numbers explode quickly (10! exceeds 3.6 million), which is exactly why they're calculated rather than counted by hand. The calculation runs in your browser with nothing uploaded. Pair it with the Logarithm and other ToolsMonk student and STEM tools for your maths coursework.
| Price | Free, no signup, no paywall, no watermark |
|---|---|
| Works on | Any modern browser: desktop, tablet, and mobile |
| Processing | In your browser, files never leave your device |
| Account required | None |
| Category | Student Tools |
Enter n (total items) and r (number chosen)
The tool calculates both nPr (permutations) and nCr (combinations)
Read the result for your problem
Use the explanation to pick the right one
Calculates permutations (nPr) and combinations (nCr)
From n (total items) and r (chosen items)
Clear results for probability and statistics
Explains when to use each
Runs in your browser, nothing is uploaded
Free, with no signup and no limit on problems
Solving permutation and combination problems
Probability and statistics homework
Counting arrangements or selections
Checking nPr / nCr values
Ask 'does order matter?', yes = permutation (nPr), no = combination (nCr)
nCr is always ≤ nPr because it ignores the duplicate orderings permutations count
Passwords/rankings = permutations; hands/groups/selections = combinations
Common questions about this tool, its workflow, and what to expect before you use it.
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Calculate P(n,r) and C(n,r) with step-by-step formulas.
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