Combinations and Permutations Calculator

Calculate combinations (nCr) and permutations (nPr) of n and r.

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How it works

Enter the total number of items n and the number chosen r. The tool computes permutations (nPr = n! / (n−r)!), where order matters, and combinations (nCr = n! / (r! × (n−r)!)), where order does not. It uses big-integer arithmetic so results stay exact even for large inputs, and shows the formulas used. These are the core counting tools of probability and statistics. All math runs locally in your browser.


              nPr = n!/(n−r)!     nCr = n!/(r!(n−r)!)

Common use cases

  • Counting how many ways to arrange or choose items.
  • Computing lottery or card-hand probabilities.
  • Checking combinatorics homework.

Frequently asked questions

What is the difference between a combination and a permutation?

In a permutation, order matters — ABC and CBA are different. In a combination, order does not — ABC and CBA are the same selection. That is why nPr is always greater than or equal to nCr.

Can r be larger than n?

No. You cannot choose more items than are available, so r must be between 0 and n. The tool flags inputs where r exceeds n.

Are the results exact for large numbers?

Yes. It uses big-integer arithmetic, so large nCr and nPr values are computed exactly without rounding.