Combinations with Repetition Calculator
Enter the number of distinct items and the selection size to calculate how many combinations exist when repetition is allowed and order does not matter.
Combinations with repetition: 35
How to Use This Calculator
- Specify the number of distinct types (n).
- Enter the size of the selection you wish to make (k).
- Read the number of combinations where repetition is allowed and order does not matter.
- Apply the result to combinatorics problems such as distributing identical items into bins.
Formula
Number of combinations with repetition = C(n + k − 1, k)
Alternative form: C(n + k − 1, n − 1)
Derived from the stars-and-bars combinatorial argument
Full Description
Combinations with repetition count the number of multisets of size k drawn from n distinct types. The classic stars-and-bars method maps the problem to placing separators among identical symbols, leading to the binomial coefficient formula.
Frequently Asked Questions
How is this different from combinations without repetition?
Without repetition, each item can appear at most once. Here, items can appear multiple times and order still doesn’t matter.
What happens if k = 0?
There is exactly one way to choose zero items: the empty selection. The calculator reports 1.
Can I use non-integer inputs?
No. Combinations are defined for non-negative integers. Inputs are rounded to the nearest integers.
Does the order of elements matter?
No. Combinations disregard order. If order matters, use permutations or other arrangements.