How this calculator works
Combinations use C(n,r)=n!/(r!(n−r)!).
Formula
C(n,r)=n!/(r!(n−r)!)Counts unordered selections of r objects from n distinct objects without replacement.
Worked example
Five choose three is a verified test case used by the calculation engine.
Assumptions and limitations
- n and r are non-negative integers with r≤n.
- Objects are distinct and selections are made without replacement.
- Results are limited to the supported exact integer range.
Methodology & sources
This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint. Technical calculation version: 1.
- CalcuMint deterministic statistics engine
Frequently asked questions
How are combinations different from permutations?
Combinations ignore selection order; permutations count different orders separately.
What is C(n,0)?
There is exactly one way to select zero objects, so C(n,0)=1.