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Combinations Calculator — result sheet
Count unordered selections of r distinct items from n items without replacement.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: C(n,r) = n! / (r!(n-r)!).
A combination ignores order, so selecting A then B is the same selection as B then A. The calculation uses the smaller of r and n-r with exact integer products rather than large floating-point factorials. Counts are returned only when representable as safe JavaScript integers.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Available items (n) — minimum 0; maximum 1000
- Items selected (r) — Cannot exceed n. Results must fit the safe integer limit.; minimum 0; maximum 1000
Worked example
| Input | Value |
|---|---|
| Available items (n) | 10 |
| Items selected (r) | 3 |
120
Assumptions and limits
- Items are distinct, selection is without replacement, and order does not matter.
- n and r are integers satisfying 0 <= r <= n <= 1,000.
- C(n,0) and C(n,n), including C(0,0), equal 1. Counts above 9,007,199,254,740,991 are rejected, not rounded.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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