Permut c/ Repetição
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The Permutations with Repetition Calculator is an online tool that calculates the number of ways to arrange objects when some of them are identical. It uses the formula for permutations with repetition, which is n! / (n₁! · n₂! · ...), where n is the total number of objects and n₁, n₂, etc., are the quantities of each type of identical object.
This formula works by dividing the factorial of the total number of objects (n!) by the factorials of the quantities of each type of identical object (n₁!, n₂!, etc.). This is useful in situations where the order of objects matters, but some of them are indistinguishable. For example, when arranging the letters of the word 'banana', the calculator takes into account that there are 3 identical letters 'a'.
It's essential to use this calculator in cases where there are repeated objects and the order is relevant, such as in anagrams, queues with identical objects, or sequences of symbols with repetitions. It helps avoid manual counting errors and provides accurate results quickly.
When using the calculator, it's crucial to be careful with data entry, ensuring that the total number of objects and the quantities of identical objects are correctly informed. Additionally, it's essential to understand the concept of permutations with repetition to correctly interpret the obtained results.
Frequently asked questions
What is a permutation with repetition?
A permutation with repetition is a way of arranging objects where some of them are identical. The order of objects matters, but identical objects are considered equal.
How does the permutations with repetition formula work?
The formula is n! / (n₁! · n₂! · ...), where n is the total number of objects and n₁, n₂, etc., are the quantities of each type of identical object.
In which situations should I use this calculator?
Use it for anagrams, queues with identical objects, sequences of symbols with repetitions, or any situation where order matters but there are indistinguishable objects.
What precautions should I take when using the calculator?
Check that the input data is correct, especially the total number of objects and the quantities of identical objects.
Is the calculator suitable for any type of object?
Yes, as long as you can identify the identical objects and the total number of objects.