Math & Science
Permutation & Combination
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Calculate permutations (nPr) and combinations (nCr) instantly. Enter n and r to get ordered arrangements and unordered selections with full factorial breakdown. Free, instant, no signup.
Come usare questo strumento
- Enter the total number of items n and the number chosen r.
- Both the permutation nPr and the combination nCr are computed.
- Read both results with the factorial breakdown.
Quick reference
| Formula | Use when | Example |
|---|---|---|
| nPr = n! / (n−r)! | Order matters | Race podium positions |
| nCr = n! / (r!(n−r)!) | Order doesn't matter | Choosing a committee |
Domande frequenti
- What is the difference between a permutation and a combination?
- A permutation counts ordered arrangements; a combination counts unordered selections. Picking 3 of 5 where order matters is nPr; where order does not matter it is nCr.
- What are the formulas?
- nPr = n! / (n − r)! and nCr = n! / (r!·(n − r)!). The combination is the permutation divided by r! to remove duplicate orderings.
- What are the limits on n and r?
- r must be no larger than n, and both must be non-negative whole numbers. Very large factorials are limited by floating-point precision.
- Is anything I enter sent online?
- No. The factorials and nPr/nCr values are computed in your browser; your inputs are never transmitted.