Permutation and Combination Calculator
Calculate nPr (order matters) and nCr (order does not) from n and r.
Reviewed by the WorldCalcs team · Methodology · Last reviewed: June 2026
Result
Permutations (nPr)
20
Combinations (nCr)
10
What is a permutation and combination calculator?
Permutations and combinations count how many ways you can pick r items from a set of n. A permutation counts arrangements where order matters (like a race podium); a combination counts selections where order does not matter (like a lottery draw). This calculator gives you both at once.
How it's calculated
For permutations (order matters): nPr = n! / (n − r)!. For combinations (order does not matter): nCr = n! / (r! (n − r)!). The "!" is a factorial — the product of all whole numbers up to that value (5! = 5 × 4 × 3 × 2 × 1 = 120). Because every combination can be arranged in r! ways, nCr is simply nPr divided by r!.
Example
Pick 2 from 5. Permutations: 5! / 3! = 120 / 6 = 20 ordered pairs. Combinations: 5! / (2! × 3!) = 120 / 12 = 10 unordered pairs. For a 5-card hand from a 52-card deck the order does not matter, so it is a combination: 52C5 = 2 598 960 possible hands.
All calculations happen in your browser. Nothing is sent, stored, or tracked.
Results are estimates and may contain errors — for general information only, not professional advice. Always verify before relying on them. Disclaimer
How to use
Enter the total number of items (n) and how many you are choosing (r). The calculator returns both the number of ordered arrangements (nPr) and the number of unordered selections (nCr).
n and r must be non-negative whole numbers with r ≤ n.