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Permutation Calculator

Enter total number of objects n, and number of selected objects to find the permutation using permutation calculator.

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The Permutation calculator uses the total number of elements and the selected items to find the possible unique sets of the chosen elements.

The npr calculator finds the possible groups of things, without repetition, using the permutation formula. The steps of the calculations are shown right below the result.

What is permutation?

Permutation is a combination with a specific order. According to Wikipedia, a permutation is;

“An arrangement of its members into a sequence or linear order”

There are two types of permutation; with and without repetition. The permutation solver finds the permutation without repetition.

In this type, the same element cannot be repeated in a combination. Say you want a combination of 4 digits from a set of whole numbers till 9. Then a combination like (4,6,4,7) would be wrong.

Permutation Formula

The formula used for permutation is:

=(n)!/(n-r)!

In this formula n is the total number of elements and r represents the selected elements of the set. 

The exclamation mark (!) is the factorial operator. Once applied on a number it multiples that number and all the positive integers that are smaller than the number. Eg: 5! = 5 * 4 * 3 * 2 * 1 = 120.

Fun fact: The universally accepted value of 0! is 1 which is hilarious considering that you multiplied no numbers.

How to find Permutation?

Besides using the math permutation calculator, you can learn to calculate permutation yourself. Keep reading to know how the permutation formula is derived. Skip to the bottom if you are interested in the solved example only.

Consider Elsa has 120 different stickers for her journal. But she can add only 2 of them and that also in a way they look aesthetic (i.e she has to follow an order). To find the total choices, she will need to find the factorial. 

5! = 120

But we only want a set of two stickers. What to do now? Well, she divides by 3! (i.e 5-2=3). This way the choices of sets she will get will have only two stickers.

Let’s see another simple example. You have 4 digits 1, 2, 3, and 4 and you want a group of 2 digits. How many choices do you get?

Let’s see, 4! is 24 but since we want a set of 2 so we divide this answer by 2! (i.e 4-2=2). The answer we get is 12. To verify, see the possible sets.

(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(4,3),(4,2),(4,1),(3,2),(3,1),(2,1).

You can see for yourself, that no more unrepeated sets can be made using these digits. This verifies the permutation formula.

Example:

Find the permutation for the following data.

n = 7

r = 3

Solution:

Write the formula.

=(n)!/(n-r)!

Put the values.

=(7)!/(7-3)!

=7!/4!

= 5040 / 24

= 210

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