Combinations with Repetition Calculator
Calculate the number of combinations with repetition allowed using the stars and bars method, free and instant in your browser.
Enter Values
Minimum 1
Minimum 0
How to use this calculator
- Enter n (types to choose from) and r (items to choose).
- Read the count.
How it works
When order doesn't matter but repeats are allowed, the count is C(n + r − 1, r).
Worked example
n=5 flavours, r=3 scoops. = 35 combinations.
Common mistakes
- Using this when order matters — that's permutations.
- Forgetting repeats are allowed (otherwise use standard nCr).
Frequently asked questions
What is a combination with repetition?
Choosing r items from n where repeats are allowed and order doesn't matter, counted as (n + r − 1) choose r — like picking scoops of ice cream.
Where is this used?
Problems like distributing identical items into groups, or selecting with replacement where arrangement is irrelevant.
What's a real example?
Choosing 3 ice-cream scoops from 5 flavours where you can repeat a flavour — 35 ways.
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Cite this tool
Zerdly. (2026). Combinations with Repetition Calculator. Retrieved from https://www.zerdly.com/tools/combinations-with-repetition-calculator/
Tip: Enter any known values to calculate the remaining results.
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