Permutation & Combination Calculator
Calculate permutations (nPr) and combinations (nCr) with step-by-step formula breakdown and large number support.
r must be less than or equal to n when repetition is disabled.
n must be a positive integer (1 to 1,000).
r must be a non-negative integer (0 to 1,000).
Permutations (nPr)
Order matters
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Combinations (nCr)
Order does not matter
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Step-by-Step Breakdown
Permutation
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Combination
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Enter n and r above to calculate permutations and combinations.
Formulae
nPr = n! / (n−r)! (without repetition)
nPr = n^r (with repetition)
nCr = n! / (r!(n−r)!) (without repetition)
nCr = (n+r−1)! / (r!(n−1)!) (with repetition)
How to use
- 1
Enter n and r
Type the total number of items (n) and the number to choose (r).
- 2
View results
Both nPr and nCr are shown simultaneously with step-by-step breakdowns.
- 3
Toggle repetition
Enable 'With Repetition' to calculate arrangements where items can repeat.
Frequently asked questions
What is the difference between permutations and combinations?
What does 'with repetition' mean?
How large can the numbers be?
Is my data sent anywhere?
Calculate permutations and combinations for any values of n and r.
See both nPr (ordered) and nCr (unordered) simultaneously with a
step-by-step formula expansion. Supports with and without repetition
modes. Uses BigInt for exact results with large numbers. All
processing runs in your browser.