When to use this calculator
Count unordered selections when repetition is allowed. Order does not matter and a type may be selected more than once.
Explore the algebra & number calculators for other questions in this topic. For a related calculation, use the Complex Number Argument Calculator: Find a complex number’s direction in the complex plane.
PUTTING IT INTO PRACTICE
Combinations With Repetition: 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 |
|---|---|
| Item types (integer) | 3 |
| Selections (integer) | 2 |
| Result | 6 ways |
- Check the input labels and enter the example values above.
- Apply the relationship: Count = C(n+k−1,k).
- The result is 6 ways, rounded for display.
How to interpret your result
Order does not matter and a type may be selected more than once.
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 combinations with repetition calculator useful?
Count unordered selections when repetition is allowed. Order does not matter and a type may be selected more than once.
How do I use the combinations with repetition calculator?
Enter item types (integer), selections (integer). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Count = C(n+k−1,k).
What should I check before using the result?
Order does not matter and a type may be selected more than once.
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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