Statistics & Probability

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Combinations with Repetition Calculator.

Calculate combinations using the stars-and-bars formula.

On-device calculationNo signup
01

Set your values

Results update as you type.

Combinations: 35

Combinations

35.000000

Results update automatically as you type.

Use Cases

Menu and product variety planning

Determine how many different combinations of items you can offer when customers can choose multiple servings or repeats, such as a build-your-own bowl with 5 toppings and 3 scoops.

Example: 5 types, 3 selections → 35 combinations

Probability and statistics practice

Quickly compute the number of possible outcomes for experiments with replacement and without order, useful for homework or data analysis.

Example: 6 types, 4 selections → 126 combinations

Frequently Asked Questions

What is combinations with repetition?
Combinations with repetition (also called multiset combinations) count the number of ways to choose a set of items where order does not matter and each item can be chosen more than once. For example, choosing 3 flavors from 5 types where repeats are allowed.
How do I use this calculator?
Enter the number of types (distinct categories) and the number of selections (how many items you pick). The calculator instantly shows the number of possible combinations, updating as you type.
What is the formula used?
The number of combinations with repetition is C(n+k-1, k) = (n+k-1)! / (k! * (n-1)!), where n is the number of types and k is the number of selections. This calculator applies that formula automatically.

Tips & Common Mistakes

Tips

  • Ensure 'Types' is the number of distinct categories, not the total items available.
  • Selections can be larger than types because repetition is allowed.
  • Use the instant result to explore how changing selections affects the number of combinations.

Common Mistakes to Avoid

  • Confusing combinations with repetition with permutations (where order matters).
  • Entering zero or negative numbers; both fields must be positive integers.
  • Forgetting that repetition is allowed, so selections can exceed types.

Last updated: August 13, 2026