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Standard combinations assume you can't pick the same item twice — but many real situations (like choosing scoops of ice cream flavors, where repeats are fine) need a different formula.
This calculator finds the number of combinations when repetition of the same type is allowed.
How it works
Enter n (the number of types available) and r (how many items you'll choose, with repeats allowed). The calculator applies the combinations-with-repetition formula, which reduces to a standard combination calculation on a larger, adjusted pair of numbers.
- Enter n (number of types available).
- Enter r (items to choose, repetition allowed).
- Click Calculate to see your results.
Examples
5 flavors, choose 3 scoops
Choosing 3 scoops from 5 ice cream flavors, where repeating a flavor is allowed, gives 35 possible combinations.
Who should use it
- Checking combinatorics or probability coursework involving repetition.
- Counting possible combinations for recipes, toppings, or configurations where repeats are allowed.
Industry applications
- Combinatorics and discrete mathematics education
- Probability and statistics coursework
Advantages
- Directly applies the stars-and-bars combinatorial technique without requiring you to derive it yourself.
- Shows the equivalent standard combination calculation the formula reduces to.
Limitations
- Only counts combinations (order doesn't matter) — for repetition-allowed problems where order matters, a different formula (n^r) applies.
Common mistakes to avoid
- Using the standard nCr formula (which assumes no repeats) when repetition is actually allowed in the problem.
- Mixing up n (types available) with r (items chosen) when entering values.
Best practices
- Confirm whether your specific problem actually allows repeated choices before picking this calculator over the standard combination calculator.
Tips
- If order matters and repetition is allowed (unlike this calculator's scope), the count is simply n^r — much simpler than the combination formula used here.