Permutação Simples n!
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
P = n!
About this calculator
The simple permutation calculator computes the number of ways to arrange n distinct elements in a sequence. Simple permutation is represented by n! (n factorial), which is the product of all integers from 1 to n. For example, for 3 elements, the number of permutations is 3! = 3 × 2 × 1 = 6. This tool is useful for counting problems where order matters.
The calculator works straightforwardly: you enter a positive integer n (typically up to 170, due to computational limits) and the system calculates the factorial using iterative multiplication. The result shows exactly how many different orderings are possible. Note that simple permutation considers all elements as distinct; if there are repetitions, you should use permutation with repetition.
Use this calculator in situations such as: determining the number of anagrams of a word without repeated letters, calculating ways to arrange books on a shelf, or solving probability problems involving ordering of events. For example, how many different queues can be formed with 5 people? The answer is 5! = 120.
Cautions: factorial grows very fast; for n=20, the result already exceeds 2.4 quintillion. The calculator may not support very large numbers due to overflow. Also, ensure that the elements are truly distinct. If there are repetitions, the calculation is not valid for simple permutation.
Frequently asked questions
What is a simple permutation?
A simple permutation is the number of ways to arrange n distinct elements in order. It is calculated as n! (n factorial).
How to calculate simple permutation manually?
Multiply all integers from 1 to n. For example, 4! = 4 × 3 × 2 × 1 = 24.
What is the difference between permutation and combination?
In permutation, order matters; in combination, order does not. For example, AB and BA are different permutations but the same combination.
Can I use this calculator for permutation with repetition?
No. This calculator is for simple permutation only, where all elements are distinct. For repeated elements, use the permutation with repetition formula.
What is the maximum n supported?
Typically up to n=170, as beyond that the result is too large to represent numerically (overflow).