Combination Calculator
Count combinations C(n, r) — selections where order does not matter — with or without repetition, exactly.
Your inputs
Results
Combinations C(n, r)
120
- Chance of one specific combination
- 1 in 120
✓Exact calculation — rounded only for display
What this calculator does
Combinations count groups, such as lottery tickets or committee choices, where order is irrelevant.
Formula and method
C(n, r) = n! ÷ (r!(n − r)!); with repetition: C(n + r − 1, r)
Worked example
Calculated by this tool with its default inputs:
Inputs
- Total items (n): 10
- Items chosen (r): 3
- Repetition allowed (multisets): No
Results
- Combinations C(n, r): 120
- Chance of one specific combination: 1 in 120
How to read the results
The chance of one specific combination is 1 in C(n, r).
Assumptions and limitations
- Exact big-integer arithmetic.
Questions
What are the odds of a 6/49 lottery?
1 in 13,983,816.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 4 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy