Combinations with Repetition Calculator

What Are Combinations with Repetition?

Combinations with repetition (also called multisets) count how many ways you can choose $r$ items from $n$ types when order does not matter and the same type may be chosen more than once. This is different from ordinary combinations, where each item can appear at most once.

Combinations with Repetition Formula

The number of combinations with repetition is:

$$C'(n,r) = \frac{(n + r - 1)!}{r!(n - 1)!}$$

Here $n$ is the number of distinct object types and $r$ is the sample size (how many items you pick). When $r = 0$, the result is $1$ (one empty selection).

How to Use This Calculator

• Enter the total number of object types $n$.
• Enter the sample size $r$.
• Read the count $C'(n,r)$ instantly.
• When $n$ and $r$ are small (up to 12), the tool also lists the generated combinations.

Example

Suppose you have $n = 5$ flavors and want scoops of size $r = 3$, allowing repeats. Then $C'(5,3) = (5+3-1)! / (3! \cdot 4!) = 7! / (6 \cdot 24) = 35$. There are 35 possible flavor combinations with repetition.

Related Tools

Explore related counting tools:

• Permutation and Combination Calculator
• Combinations Permutations Calculator
• Probability Calculator