Combinação com Repetição
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
C_{n+k−1}^kAbout this calculator
The combination with repetition calculator solves counting problems where order does not matter and each element can be chosen more than once. It calculates the number of ways to select k items from a set of n distinct types, allowing repetitions. The formula used is C(n+k-1, k), which is the binomial coefficient of n+k-1 choose k. For example, choosing 3 ice cream flavors from 5 available, allowing repeats, the number of combinations is C(5+3-1, 3) = C(7, 3) = 35.
This tool is useful in many areas such as mathematics, statistics, computer science, and logistics. For instance, distributing 10 identical balls into 4 distinct boxes is a combination with repetition problem. It is also applied in problems of anagrams with repeated letters, combinations of items in buffets or menus, and analysis of genetic trait combinations. Simply enter the values of n (number of types) and k (quantity to choose) to get the result instantly.
Important considerations: ensure that order does not matter and repetition is allowed. If order matters, use arrangement with repetition. If no repetition, use simple combination. Also, check that n and k are non-negative integers; negative or non-integer values are not meaningful in this context. The calculator can also help understand complex counting problems, making combinatorics learning easier.
Frequently asked questions
What is the difference between combination with repetition and simple combination?
In simple combination, each element can be chosen only once. In combination with repetition, you can choose the same element multiple times.
How do I use this calculator to distribute balls into boxes?
Enter the number of boxes as n and the number of balls as k. The result is the number of ways to distribute the balls, assuming balls are identical and boxes are distinct.
Can I use decimal values for n or k?
No, n and k must be non-negative integers. Decimal values are not meaningful in the context of counting combinations.
What if I want to consider order?
If order matters, use the arrangement with repetition calculator. Combination with repetition is only for cases where order does not matter.
Does this formula work for n = 0?
Yes, if n = 0 and k = 0, the result is 1 (one way to choose nothing). If n = 0 and k > 0, the result is 0, as there are no types to choose from.