Created By : Vaibhavi Kumari
Reviewed By : Phani Ponnapalli
Last Updated : Apr 02, 2023

Total Number of Objects(n)
Sample Size(r)
Permutations Without Repetitions
Permutations With Repetitions

What is meant by Permutation in Probability ?

The definition of permutation is an arrangement of set of objects, in the matter of the order of the arrangement. In short, the objects or elements of sets are positioned in a sequence or linear order.

For instance, let's see how many ways we can arrange 2 letters from the set of three letters ie., A, B, C. Each possible arrangement would be an instance of a permutation. So, the entire list of possible permutations would be: AB, AC, BA, BC, CA, and CB.

Representation of Permutation

We can symbolize permutation in various ways. They are as follows:

  • P(n,r)
  • Pnr
  • nPr
  • nPr
  • Pn,r

Permutation Formula

The formula for permutation of n objects for r selection of objects is determined by:

For no repetitions, the formula is P(n,r) = n!/(n-r)!
For repetitions, the formula is P(n,r) = nr


  • p is the number of permutations
  • n is the number of objects
  • r is the number of chosen objects
  • ! is a factorial of a number

Detailed Process on Finding Permutations Manually

Following are the simple steps to calculate the permutations which are required to follow while solving the problems manually:

  • Firstly, we have to identify the n and r values from the given problem.
  • Next, apply the permutation formula with or without repetition as per the requirement.
  • Substutite the n and r values in the formula of permutation and solve the permutation of a given set of numbers easily and effortlessly.


Six people are playing a game. One will be chosen first, followed by other four positions. How many various ways can the position be filled?


Identify the n and r values from the above scenario. There are six people and only five positions are available. Hence, n=6 and r=5:

Put the values in the permutation formula:

nPr or P(n,r) = n!/(n-r)!

= 6! / (6-5)!

= 6! / 1!

= 6!

= 6x5x4x3x2x1

= 720

Therefore, the position can be filled in 720 ways.

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FAQs on Permutation nPr Calculator with Steps

1. How do you calculate Permutations?

How to calculate permutations, In order to calculate the permutations, identify the number of possibilities for every event and then multiply that number by itself X times. Later on, you can verify the answer using our free online permutation calculator.

2. What is a permutation in maths?

A permutation is a set of objects arranged in a definite order. In permutation, the most essential thing is ordering as it is also considered as an ordered combination.

3. What are the types of permutations?

A permutation is classified into three different categories:

  • When repetition is allowed,
  • When repetition is not allowed, and
  • When the objects are not distinct.

4. What is the formula of permutation when repetition is not allowed?

When the permutation is without repetition, the number of available choices will get decreased each time. If n is a positive integer and r is a whole number, such that r<n, then P(n,r) = n!/(n-r)!

5. How can I find the permutation calculator online?

Visit the web portal and tap on the permutation calculator link to find the permutations in split seconds with steps. Permutations calculator, npr permutation formula, npr formula calculator,  npr probability and npr permutation are available in online.