Permutation & Combination Calculator

Compute nPr and nCr with clear steps and explanations

🧮

Permutation & Combination Calculator

Calculate permutations (nPr) and combinations (nCr) for given values of n and r. This calculator considers the case without replacement (without repetition).

🧮 Compute nPr and nCr

📊 Result

Permutations, nPr
= 30
Combinations, nCr
= 15

This calculator considers permutations and combinations without replacement (no repetition).

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Permutations

Permutations are selections where order matters. We compute r-permutations of n without replacement (no repetition).

nPr = n! / (n − r)!

Example: choosing a team captain and goalkeeper from 11 players. Order matters (captain first, then goalkeeper), and the same person cannot fill both roles. This yields 11 × 10 = 110 possible outcomes, which equals 11P2.

Combinations

Combinations are selections where order does not matter. They are permutations with redundancies removed.

nCr = n! / (r! × (n − r)!)

Example: choosing 2 strikers from a team of 11. The order of selection does not matter, so divide by 2! to remove the two orderings, yielding 11C2 = 55.

With replacement (repetition) formulas (not computed by this tool): nPr with replacement = n^r. For combinations with replacement: (r + n − 1)! / (r! × (n − 1)!).