A combination is a selection of r elements from a set of n, where the order of selected elements does not matter. For example, choosing 2 fruits from {apple, pear, grape} gives 3 combinations: {apple, pear}, {apple, grape}, {pear, grape}.
Combination Calculator
Calculate C(n,r) and combinations with repetition. Formula, steps, and BigInt result.
Combinations without and with repetition with exact results.
A combination is a count of subsets of r elements chosen from n, where order does not matter. Without repetition, C(n,r) = n! / (r!(n-r)!). With repetition (multiset combination), CR(n,r) = C(n+r-1, r). The tool uses BigInt for exact results even for large values.
Enter n and r, then choose the combination mode.
- Enter n (total available elements) and r (elements to choose).
- Select 'Without repetition' for C(n,r) or 'With repetition' for CR(n,r).
- Check the result, the applied formula, and the calculation steps.
Sources and references for this tool
These references help contextualize formulas, standards, APIs and limitations used on this page. They do not replace professional validation when a result has legal, financial, medical or operational impact.
- Combinatorics — NIST Digital Library of Mathematical FunctionsNIST — Definitions and identities for combinations, permutations and related functions.
- Pascal's Triangle — Wolfram MathWorldWolfram MathWorld — Context on Pascal's triangle and its relation to combinations.
- BigIntMDN Web Docs — API used to calculate combinations for large n and r without overflow.