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Combinations With Repetition — result sheet
Count unordered selections of a fixed size from reusable types, where selecting the same type more than once is allowed.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: C(n + r - 1, r) = (n + r - 1)! / (r!(n - 1)!).
This counts multisets: changing the order of the selected types does not make a new outcome, but a type can be used repeatedly. It is different from an ordinary combination, which selects distinct items without replacement.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Available types (n) — minimum 1; maximum 1000
- Selections (r) — A type may be selected repeatedly; the exact result must fit the safe integer range.; minimum 0; maximum 1000
Worked example
| Input | Value |
|---|---|
| Available types (n) | 5 |
| Selections (r) | 3 |
35 unordered selections of 3 items from 5 reusable types.
Assumptions and limits
- n is the number of distinct reusable types and r is a nonnegative selection count.
- Selections are unordered and repetition is allowed for every type.
- Counts above JavaScript's exact safe integer range are rejected instead of 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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