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Combinations Without Repetition Calculator — result sheet
Count how many unordered groups of a chosen size can be selected from a finite set without repeating an item.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: C(n,r) = n!/[r!(n-r)!].
A combination treats the same selected items as one group regardless of order. The calculator uses a logarithmic factorial product to keep integer results stable for practical n values.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Available items n — minimum 0; maximum 170
- Items selected r — minimum 0; maximum 170
Worked example
| Input | Value |
|---|---|
| Available items n | 10 |
| Items selected r | 3 |
There are 120 unordered groups of 3 from 10 items.
Assumptions and limits
- Items are distinct, selection order does not matter, and no item can be selected twice.
- r is a whole number from zero through n; the result is an exact integer within the supported range.
- This counts possible groups and does not assign probabilities unless a separate random-selection model is specified.
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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