Permutation & Combination Calculator
NewCalculate nPr (permutations) and nCr (combinations) for a given n and r, with exact BigInt precision and the formula shown step-by-step.
Permutations count arrangements where order matters (nPr = n! / (n−r)!); combinations count selections where order doesn't (nCr = n! / (r!(n−r)!) = nPr / r!). Both use exact BigInt arithmetic so results stay precise even for large n.
Frequently Asked Questions
What's the difference between permutations and combinations?
Permutations (nPr) count arrangements where order matters — like assigning 1st, 2nd, and 3rd place medals. Combinations (nCr) count selections where order doesn't matter — like choosing 3 people for a team, where the order you pick them in doesn't change the resulting team.
Why does the tool use BigInt for the calculation?
Factorials grow extremely fast — 20! already exceeds 2.4 quintillion — so regular JavaScript numbers would lose precision well before reaching the 1000! cap this tool allows. BigInt keeps every digit exact.
What happens if I set r greater than n?
The tool shows an error, since you can't choose or arrange more items than actually exist in the set — both nPr and nCr are undefined (or zero, by convention) when r > n.
How is nCr derived from nPr?
nCr = nPr / r! — dividing out the r! ways to order any given selection removes the order-dependence, converting the "arrangements" count into a "selections" count.
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