Combinations Calculator
C(n,k) = n! ÷ (k!(n − k)!)
Count unordered selections without replacement from distinct items.
Formula
C(n,k) = n! ÷ (k!(n − k)!)
Worked example
Available items: 10
Items selected: 3
With these inputs, the result is **120 **.
How to use this calculator
- Identify the quantity you want to calculate.
- Enter your measurements in the units shown on each field.
- Read the result, which updates as you change the inputs.
- Check the assumptions below before applying the result.
Assumptions and limits
Order does not matter. This uses floating-point arithmetic and may lose integer precision for large counts.
Precision and checking
Results are rounded for display. Use the most accurate measurements available, and avoid rounding your inputs unnecessarily. Extra decimal places in a result do not make an estimate more reliable.
To check a result, substitute the same input values into the formula shown above. Change one value at a time to understand how the quantity responds.
Frequently asked questions
What assumptions does this calculation use?
Order does not matter. This uses floating-point arithmetic and may lose integer precision for large counts.
Are my inputs sent to a server?
No. The calculation runs locally in your browser. The result updates as you edit the inputs.
