Permutation calculator

When we talk about permutations we are taking into account the order of the elements of the set, that is, it is an ordered combination. It is important not to confuse permutations with combinations, since in the latter the order does not matter.

To make it easier for you to calculate permutations online we have created a calculator that takes into account whether the permutation is with repetition or without repetition. If you have doubts about which one to use in each case, read on.

Permutations with repetition

A permutation with repetition is the one in which we have n elements that we take a number of r times.

As this is a permutation with repetition, if we pick up an element, it can come back out again in the second election and so on until reaching r times.

The formula for permutations with repetition is nrbeing:

  • n the number of elements of the set
  • r the elements we choose

Like practical example Let's imagine that we have a set with the numbers from 1 to 6. How many permutations are there if we take 3 of them? We apply the above formula and we have that

nr = 63 = 6 x 6 x 6 x 6 = 216 permutations

Why is this example a case of permutation with repetition? Basically it is because if we throw a number and it comes out a 2, in the next round that same number could also come out again. Therefore, there is repetition in the set of elements.

Permutations without repetition

It may also be the case that we are faced with a permutation without repetition. This means that once one of the elements of the set has left, it cannot reappear.

This means that if you have 10 chances of something happening, in the next round you will have 9, in the next round you will have 8 and so on.

In this case, the formula for permutations without repetition is as follows:

Formula of permutations without repetition

Again we have that 'n' is the number of elements and 'r' are the ones we choose.

As you can see, in this formula we need to know well what is the factorial of a number since it is an essential mathematical concept to be able to calculate well the permutation without repetition.

We are going to see a example.. Imagine that you have four balls, each one with a different color and we are going to keep 2. We apply the above formula and we have that:

(4 x 3 x 2 x 1) / (4 - 2)! = 24 / 2 = 12 permutations

That is, there are 12 different possibilities to choose 2 balls from a set of four.

Circular permutations

The circular permutations are those used when the elements of the set are arranged in a circle, i.e., the first element of the sample is also the last one.

A clear example to understand what circular permutations are is to imagine a round table around which several people are seated. We choose one of them to be the first element and this will be the beginning and the end of the sample.

In this case, the formula for circular permutations es:

PCn = (n - 1)!

Where n is the number of elements of the set.

Returning to the example of the round table, let's imagine that we have to seat 5 diners for dinner. How many ways are there to seat them? To calculate it, we apply the formula above:

PCn = (n-1)! = (5 - 1)! = 4! = 24

Calculating permutations on the calculator with nPr

The Casio calculator and other brands come with a function that allows you to calculate permutations with ease.

In the case of Casio scientific calculators, this function is called nPr and is used to calculate permutations without repetition.

In general, to use the nPr function of your calculator you have to:

Insert value of n > Shift > nCr key with secondary function nPr > type the value of r

The use of these or other keys depends a little on the model of Casio calculator you have.

Permutation in Excel

If you want to calculate a permutation in ExcelIf you use a formula with or without repetition, you will have to use one formula or another depending on whether it is with repetition or without repetition.

With repetition

The function will return the number of permutations for a given number of elements with repetitions that can be chosen from the total set.


No repetition

This is the case of permutations without repetitionn, this is the formula to use in Excel:


In both cases the values of n and r must be replaced by the corresponding number or the corresponding cell in which their values are reflected.

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