Combination calculator
Count the ways to choose r distinct items from n items when order does not matter and repetition is not allowed.
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| Total items n | Use a whole number in the stated format. Fractions and rounding are not interchangeable with exact integer inputs. |
| Items selected r | Use a whole number in the stated format. Fractions and rounding are not interchangeable with exact integer inputs. |
Understanding your result
Read Combinations in the units and model stated on this page. The formula C(n, r) = n! ÷ (r! × (n − r)!) defines the relationship; measurement accuracy and model applicability are separate from numerical precision.
Common mistakes
- Using a different mathematical definition or operation than the one stated by this tool.
Check your calculation
- Use the worked example as a known reference case, then change one input at a time and check the direction and units of the response.
Calculation checks, sources and review limits
How many groups can I choose when order does not matter?
Enter the total number of distinct items and how many you select. Selecting the same group in a different order does not create a new combination.
Common uses
- Count possible selections from a set.
- Compare group sizes in a combinatorics problem.
How it works
Combinations treat each selected group as one outcome, regardless of order. Use whole numbers from 0 to 1,000 with r no larger than n. Choosing no items or all items gives one combination. Arithmetic stays exact even for very large answers.
Worked example
Choosing 3 items from 10 gives 10! ÷ (3! × 7!) = 120 combinations.