Best Way to Understand the Permutation Formula and Find the Permutation with Examples

Introduction

Permutation is a statistical concept that helps to find the number of possible arrangements of a set. In this article, you will learn what permutation formula is and how to find permutation.

What is Permutation?

It is a mathematical technique that calculates the number of possible arrangements in a set when the order of arrangement matters. A permutation is an arrangement in a definite order of a number of objects taken some of all at a time.

For example, the arrangement of the letters of word: ROSE. The possible arrangement of this word is ROSE, ROES, RSEO,… which is said to be a permutation of ROSE. Similarly, if we write the arrangement of ROSE with only two letters i.e. RO, then it will be the permutation of ROSE with two letters at a time.

Permutation Formula

A permutation is used to find the possible arrangement of numbers in a set with a specific order. The total elements and the selected number of elements are used to calculate permutation. The general permutation formula can be expressed as:

Permutation Formula with Repetition

Since we know that the permutation is the number of possible arrangements in a specific order. Permutation with repetition means the selection of one element can be twice as long. The permutation with repetition formula is,

$$P\;(n\;,\;r)\;=\;nPr\;=\;n^r$$

How do you find permutation?

You can calculate permutation of any set of elements by using the permutation formula. So, if there are n number of elements and r number of elements to be selected, then the permutation formula is:

$$P\;(n\;,\;r)\;=\;nPr\;=\;\frac{n!}{(n\;-\;r)!}$$

You can use the following steps to find permutations in an easy way.

1. Find the factorial of the total number of elements.
2. Subtract the selected number of elements from the total number of elements.
3. Find the factorial for the remaining number.
4. Now, find the ratio of n! and n-r!

Here are some examples to understand how to calculate permutation.

Formulas Related to Permutation Formula

Combination Formula

It is used to find the expected combination of any data set without considering the order of data. The formula is:

$$^nC_r \;=\; \frac{n!}{r! (n-r!)}$$

Where,
n= total number of elements
r= the number of selected elements
!= factorial

Probability Formula

It is used to find the occurrence of a sample data when some of them are selected. The probability formula is:

$$P(A) \;=\; \frac{n(A)}{n(S)}$$

Where,
P (A) = is the probability of an event A
n(A)= is the number of possible outcomes.
n(S)= is the number of total outcomes.

Where is Permutation Used?

A permutation is used to find the number of possible arrangements for the data for which the order of arrangement matters. It helps to find all possible arrangements with the permutation formula.

Who Discovered the Permutation Formula?

In the 17th century, the French mathematicians Blaise Pascal and Pierre de Fermat invented the theory of probability and permutation.

Alan Walker

Last updated: July 07, 2023

Studies mathematics sciences, and Technology. Tech geek and a content writer. Wikipedia addict who wants to know everything. Loves traveling, nature, reading. Math and Technology have done their part, and now it's the time for us to get benefits.