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Combination & Permutation Calculator
Calculate nCr (combinations) and nPr (permutations) with step-by-step formula.
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Combinations & Permutations
Combinations (nCr)
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Permutations (nPr)
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Step-by-Step
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How to Use
- Enter n — Total number of items in the set.
- Enter r — Number of items to choose.
- Calculate — View nCr (combinations) and nPr (permutations) with step-by-step formula.
What are Combinations and Permutations?
Permutations (nPr) count the number of ways to arrange r items from a set of n items where order matters. For example, the number of ways to arrange 3 books from 10 on a shelf.
Combinations (nCr) count the number of ways to select r items from a set of n items where order does not matter. For example, the number of ways to choose 3 team members from 10 candidates.
Frequently Asked Questions
What is the difference between nCr and nPr?
nCr (combinations) counts selections where order does not matter. nPr (permutations) counts arrangements where order matters. nPr is always larger than nCr for the same n and r (when r > 1).
What happens when r > n?
When r is larger than n, both nCr and nPr are 0 because you cannot choose or arrange more items than available.
What is the maximum value for n?
Values up to 170 are supported. Beyond that, factorial results exceed JavaScript's maximum safe integer (Number.MAX_SAFE_INTEGER).
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