Calculate permutations (nPr) and combinations (nCr).
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How do you calculate permutations and combinations?
nPr = n! ÷ (n − r)! counts ordered arrangements, and nCr = n! ÷ (r! × (n − r)!) counts unordered selections. Permutations are always at least as many as combinations because order adds extra arrangements. For example, from 5 items choosing 2 gives 10 combinations (5C2) and 20 permutations (5P2).
Understanding your result
Permutations are always at least as many as combinations, because order adds extra arrangements.
Formula and method
nPr = n! ÷ (n − r)! counts ordered arrangements. nCr = n! ÷ (r! × (n − r)!) counts unordered selections.
Worked example
From 5 items choosing 2: 10 combinations (5C2) and 20 permutations (5P2).
How to use this tool
- Enter n (total items) and r (how many you choose).
- Read both nCr and nPr.
Common mistakes to avoid
- Using r greater than n — you cannot choose more items than you have.
About the Permutations & Combinations
Calculate how many ways you can choose or arrange items: combinations (order does not matter) and permutations (order matters).
Who should use this tool
Students and anyone working with probability or counting problems.
Frequently asked questions
What is the difference between nPr and nCr?
nPr counts ordered arrangements; nCr counts unordered selections.
What is the largest n supported?
Up to 170, beyond which factorials exceed the number range.