Permutations & Combinations Calculator (nPr, nCr)
Use this free permutations and combinations calculator to count arrangements and selections. Enter n and r to get both nPr (order matters) and nCr (order doesn’t), with the factorial formulas shown.
The formulas
Permutations: nPr = n! / (n − r)!. Combinations: nCr = n! / (r!·(n − r)!). The calculator substitutes the factorials and simplifies.
When to use which
Use permutations when order matters (like a race finish), and combinations when it doesn’t (like a committee).
Frequently asked questions
What is the difference between a permutation and a combination?
In a permutation the order matters; in a combination it doesn’t. nPr counts ordered selections, nCr counts unordered ones.
What does nCr mean?
The number of ways to choose r items from n when order doesn’t matter: nCr = n!/(r!(n−r)!).
Can it handle large numbers?
Yes — it uses exact integer arithmetic so results stay precise for large n and r.
Read the full lesson: learn the method step by step.
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