🎲 Permutations (nPr) & Combinations (nCr) Calculator
Calculate permutations nPr (order matters), combinations nCr (order does not matter), and factorials with step-by-step probability formulas.
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Combinations nCr (Order Does NOT Matter)
56
e.g. Committee groups, lottery picks
Permutations nPr (Order DOES Matter)
336
e.g. Passwords, race rankings
nCr = 8! / [3! × (8-3)!] = 56
nPr = 8! / (8-3)! = 336
How to Use Permutations (nPr) & Combinations (nCr) Calculator
- Enter total number of elements n and sample subset size r (where r ≤ n)
- Review calculated combinations nCr and permutations nPr totals
- Inspect mathematical step-by-step factorial formulas
📖 Technical Encyclopedia & Standards Reference
Calculate permutations nPr (order matters), combinations nCr (order does not matter), and factorials with step-by-step probability formulas. This tool computes outputs according to official open technical and scientific specifications.
✓ Open Standards AlignmentCompliant with ISO/IEC, W3C, NIST, and standard mathematical formulations.
✓ 100% Client-Side / SecureZero server logging. Computations execute entirely in your local browser sandbox.
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Frequently Asked Questions
What is the fundamental difference between Permutations and Combinations?
Permutations (nPr) count arrangements where the order of items matters (e.g. passwords, race results). Combinations (nCr) count selections where order does not matter (e.g. card hands, team committees).
What are the mathematical formulas for nPr and nCr?
nPr = n! / (n - r)! and nCr = n! / [ r! × (n - r)! ].