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Permutation Calculator


The advanced permutation calculator finds the number of subsets that can be taken from a large set. Our NPR calculator allows you to calculate the subsets that include the subsets of the same items in different orders.

What Is Permutation?

The permutation is the process to compute the elements of a set into the subset where the arrangement of the elements is important within the order.

Permutation Formula: 

Our permutation calculator cuts your hassle in half when it comes to calculating and arranging the elements of the sets into the subsets. To calculate the possible number of permutations of r non-repeating elements from a set of n elements, the formula is as follows:

P(n,r) = n! / (n - r)! 

nPr =  n! / (n - r)! 

For n ≥ r ≥ 0


  • r is the value of the sample size
  • n is the number of the objects 

When n = r this reduces to n!, a simple factorial of n. 

You can use our factorial calculator to find out the factorial (!) of any real number. 

How To Calculate Permutations?

Permutation is the way to choose r from the n elements. The Permutation Calculator finds the number of permutations that can be created including subsets of the same items in different orders in a matter of seconds. 

However, we will demonstrate permutations with examples so that you can grasp the concept easily. 


There is a race challenge between the 12 students in school, you believe that you know the best 4 students and that 3 of them will finish in the top spots: (1st, 2nd, and 3rd). So out of that set of 4 guys, you want to pick the subset of 3 winners and the order in which they finish. 

How many different permutations are there for the top 3 of the 4 best undergraduates?


Given data:

(r) = 3 
(n) = 4 

Looking for an ordered subset of 3 students (r) from the set of 4 best racers (n). Here you can ignore the other 8 students in this race of 12 because they do not apply to our problem. You must calculate P(4,3) to find the total possible outcomes for the top 3 winners.

Permutation Equation:

P(n,r) = n! / (n - r)! 

Find the n!

(!) means that multiply the sequence of numbers from 1 to that number.

4! = 1 * 2 * 3 * 4 = 24

Find the (n-1)!

= (4-3)! = 1!

Put the values in the NPR formula:

P(4,3) = 24 / 1 = 24 

Working Of Permutation Calculator: 

Our permutations calculator is loaded with a user-friendly interface that reports the results within a couple of seconds. It aid’s in determining the elements in the subsets. Take a look at the following points:


  • Put the value of the sample size (r)
  • Put the value of the number of objects (n) 
  • Tap “calculate”


  • Permutation of the given number 
  • Step-by-step solution

Permutation vs Combination:

Permutation and combination both are different methods to arrange the elements of the sets into the subsets.

Unlike permutation, the combination is also a way of arranging the elements of a large dataset but without considering the order, and you can find combinations by our combination calculator

As we above discuss the example of permutation, in a team of racers the order of the winners is important. If all three winners will be blessed with the same prize and it’s not important who is at the top then the winners would be considered as a combination.  


What Is 3 P 2?

In this case, permutations are the way to calculate the number of permutations that can be achieved from three. Therefore 3 P 2 is equal to 6. 

What Are The Uses Of Permutation In Different Fields?

A permutation is used to give the sequence of elements of the set to the subsets. The uses of the permutation in the various fields are as follows:

  • In computer science for analyzing sorting algorithm
  • In quantum physics, describing the state of the particles 
  • In biology, for describing the RNA sequences 

How Many Permutations Are In 6?

There are 720 different permutations of 6. 


From the source Wikipedia: Permutation, History, Permutations without repetitions, Definition, Notations, Other uses of the term permutation, Properties, Permutations of totally ordered sets, Permutations in computing.