Combinations & Permutations Calculator
Count ways to select or arrange items without replacement, with exact combination and permutation results.
Your result
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How to use this calculator
- Enter your values in the labeled fields, keeping the displayed units.
- Choose Calculate or press Enter in a single-line field.
- Review the result and the assumptions below before using it.
Formula and method
Combinations C(n,r) = n! / (r! × (n−r)!). Permutations P(n,r) = n! / (n−r)!.
Worked example
Selecting three of ten items gives 120 combinations or 720 ordered arrangements.
What the result assumes
Items are distinct and cannot be repeated. Selecting zero items has one outcome: the empty selection.
Common question
What is the difference between combinations and permutations?
Combinations ignore order; permutations count different orders separately.