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mathClassic tool

Permutation and Combination Calculator

Calculate nPr and nCr to compare ordered arrangements and unordered selections.

Use this permutation and combination calculator to count how many ways items can be arranged or selected without repetition. It is useful for combinatorics homework, probability practice, contest scenarios, team building, seating plans and any task where you need a reliable count of possibilities.

Enter the total number of available items in n and the number selected in r. The tool returns nPr when order matters, such as podium places, passwords or ranked positions, and nCr when only the chosen group matters, such as committees, lottery picks or bundle choices.

Because these totals grow very quickly, the calculator keeps exact integer results instead of rounding them. If r is greater than n or the input contains decimals or text, the page flags the issue before you rely on the count.

Quick example: with n = 10 and r = 3, there are 720 ordered arrangements and 120 unordered combinations.

Permutations (nPr)—
Combinations (nCr)—
When order mattersFill in n and r to calculate the number of possibilities.
When order does not matterFill in n and r to calculate the number of possibilities.
Applied formulasnPr = n! / (n - r)! | nCr = n! / (r! × (n - r)!)

Use clear inputs to get a more useful result.