When to use this calculator
Use combinations for choosing committees or groups: selecting A then B describes the same selection as B then A.
Explore the algebra & number calculators for other questions in this topic. For a related calculation, use the Combinations With Repetition Calculator: Count unordered selections when repetition is allowed.
PUTTING IT INTO PRACTICE
Combination: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Available items (integer) | 10 |
| Chosen items (integer) | 3 |
| Result | 120 ways |
- Check the input labels and enter the example values above.
- Apply the relationship: Combinations = n! ÷ (k!(n − k)!).
- The result is 120 ways, rounded for display.
How to interpret your result
Items must be distinct, no replacement is allowed, and k cannot exceed n. Large answers may be approximate.
Identify whether the question asks for one term, a total or a count of possible selections. Sequences use a fixed difference or ratio. In counting problems, order and replacement determine the correct model.
Frequently asked questions
Do combinations and permutations count the same thing?
No. Combinations ignore the order of selection; permutations count different orders separately.
When is the combination calculator useful?
Use combinations for choosing committees or groups: selecting A then B describes the same selection as B then A.
How do I use the combination calculator?
Enter available items (integer), chosen items (integer). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Combinations = n! ÷ (k!(n − k)!).
What should I check before using the result?
Items must be distinct, no replacement is allowed, and k cannot exceed n. Large answers may be approximate.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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