Skip to main content

Permutation and Combination

Permutation and Combination


Hey guys, I am back with one more interesting mathematics topic. And I am pretty sure that you guys would find it interesting too because many of you must have faced problems regarding these arrangements. Although if you were not able to solve them at that moment of time I am sure after completing this article you would solve the problem in minutes or even seconds.



WHAT IS THE DIFFERENCE ??
Many people get confused between these two terms permutation and combination. They both have almost similar use but have a vast difference in their meaning. You may think that both of them mean arranging entities, then what is the difference ?? For making it easy we will take an example, lets say I have four friends : Arya, Bhavesh, Chirayu and Dhruv. So if I arrange them like Arya, Bhavesh, Chirayu and Dhruv or Dhruv, Chirayu, Bhavesh and Arya, it will make no difference in combinations but if you check them according to permutation they will be different. As the difficulty of the name suggests permutation is more complex and combination much simpler. In permutation every single detail and order matters while in combination such small details and order do not matter much.


PERMUTATION
So now let us know how can we solve these questions. Continuing the same example I add 5 more names in it. So now the total number of friends I have is 9. They are:


  1. Arya 
  2. Bhavesh
  3. Chirayu
  4. Dhruv
  5. Eshaan
  6. Faraahat
  7. Gaurav
  8. Himal
  9. Ishaan
Here are the names of a few car which i will be giving them :- Audi,Honda City and Alto, let us see how many ways are there by which I could do this.( Don't forget the order ) For making it simpler we name all of them as A B C D E F G H I

            A    B   C   D    E   F   G   H    I        Total 9 options
   
So for the first car i.e. Audi I have 9 options I could give it to anyone from
A B C D E F G H I
Suppose I give it to A , then I am left with 8 options


          B   C   D    E   F   G   H    I        Total 8 options

  Now I could give Honda City to anyone of these 8.
Suppose I give it to B,
then I am left with 7 options 


                     C   D    E   F   G   H    I        Total 7 options

    Now I could give Alto to any of these 7.
   Suppose I give it to C


 
            Now time for the total calculation of the options. First we had 9 options then 8 options and at the last we were left with only 7 options. So the total options are 9*8*7 = 504.
This 504 means that we could give these three cars in 504 ways and also none of them repeating. Have you ever thought that these 3 cars would take upto 504 ways.

As we know that
                              9! ( ! - this means factorial) = 9*8*7*6*5*4*3*2*1

                               But we only want 9*8*7
                               So why to waste our time on 6*5*4*3*2*1 , let us remove it
                              6*5*4*3*2*1 = 6!
                         
                                  Finally what we get is
                                                                =  9! / 6!
                                                                =  9! / (9-3)!

   So consider the total number of entities to be "n" and the quantity we want to pick in order "r"
     From this long and a bit confusing derivation we got the formula


                                                              n! / (n-r)!

  So finally this is the universal formula for permutation where total entities are "n" and the ways to arrange "r" entities in order is

                                     P(n,r) = n! / (n-r)!
So I hope you got to know more about permutation and I promise in my next article you will also get to know more about Combinations. Thanks a lot for reading this article and spending your valuable time on this article.


You may also like these articles from High School Pedia:


To know more about Combinations check this out : Combinations

Enjoy your high school with - High School Pedia : www.highschoolpedia.com
Labels:

Comments

  1. Emma Jasmine2 December 2020 at 16:55

    Permutation and Combination is basically the various ways in which object from a particular set may be selected, without replacement, to form subsets. When the order of selection is factor the selection of Subset is called permutation and when the order of selection is not a factor then it is called combination. You explained this topic in a very easy manner like my maths home tutor was used to explain when I was doing my high school studies. I hired him for my h2 math tuition from an online website.

    ReplyDelete
  2. Nisha8 June 2021 at 16:05

    thanks for sharing the nice post about high school pedia. It is useful information about the students Child concentration exercises
    Concentration Exercises For Students
    English coaching centre in chennai
    Maths tuition in chennai
    Brain development in chennai

    ReplyDelete
  3. deepashree9 September 2022 at 10:25

    This service admired me. .Home Interior Designers In Chennai also, provides extraordinary services. Please visit to enjoy mesmerizing services.

    ReplyDelete
  4. Lakshmi14 September 2022 at 10:14

    This comment has been removed by the author.

    ReplyDelete
  5. Lakshmi3 November 2022 at 10:30

    This comment has been removed by the author.

    ReplyDelete

Post a Comment

Popular Posts

Android Versions Named After Sweet

Have you ever thought why are Android versions always named after sweet names ?? Everytime a new Android version is launched its name is kept after a sweet name. Many people have researched about this topic and many have asked Google also. Have you ever tried to find out the core reason behind this? If not then you would find the answer here . First of all let us first see what Google says about this : In 2008 i.e. the year when Android was launched a reporter asked the reason for the same. At that time Google said “It’s kind of like an internal team thing, and we prefer to be a little bit — how should I say — a bit inscrutable in the matter, I’ll say,” said Randall Sarafa, a Google spokesman. “The obvious thing is that, yeah, the Android platform releases, they go by dessert names and by alphabetical order for the most part."
14 comments
Read more

Paid Apps For Free ??

Everyone wants to play a game like GTA on iPad, it is easy on a computer to download such games but difficult on smart devices like iPad, tablet,  or smartphones. We can buy them but not everyone can buy games. But no worries guys there is a solution to this problem where one can have fun of playing games without spending their precious money .(underlined apps have downloading links  given at the end) iOS There many apps through which you can download these paid games for free. Also, there are many sites for the same. One of the most helpful apps is a Chinese app.It is called haimawan. If on a ios device, then you just have to click install which will redirect to settings  add a profile  and boom enjoy it as you wish . but it does not always work, it might work for few days and then the verification problem which may not cure. One more app is tutu which is a fantastic app and always work (99.9% sure .. nothing is perfect). X cross was the perfect app b...
14 comments
Read more

Animal and Plant Cells

 Cells Cells are the basic functional, biological and structural unit of life. The word cell is a Latin word meaning ‘small room’. Cells are also known as building blocks of life.  The branch of science that deals with the form, structure, and composition of a cell is known as Cytology. All organisms around us are made up of cells. Bacteria, ameba, paramecium, algae, fungi, plants and animals are made up of cells.  Cells together form tissues. And tissue together makes an organ. History Of Cell The cell was discovered by Robert Hooke in 1665. He assembled a simple microscope and observed a very thin slice of cork under his primitive microscope. The cork was obtained from the outer covering of a tree called bark. Robert Hooke observed many little-partitioned boxes or compartments in the cork slice. These boxes appeared like a honey-comb. He termed these boxes as the cell. He also noticed that one box was separated from another by a wa...
23 comments
Read more

Important Mathematical Constants!

Important Mathematical Constants Mathematical constants are those numbers that are special and interesting because they come up in the various fields of mathematics like geometry, calculus etc. These mathematical constants are usually named after the person who discovered it and they are represented by a symbol that is usually picked up from the Greek alphabet. Mathematical constants are by definition very important. In this article we will take a look at certain mathematical constants that are more commonplace than others. 1.       π (pi) or Archimedes constant (~3.14159):   π is defined as the ratio of the circumference of a circle to its diameter. This is probably the most popular mathematical constant. So π is the circumference of the circle whose diameter is 1 unit. You might have seen it popping up when calculating the area of a circle (πr 2 ) or the circumference of a circle (2πr). It has many uses throughout mathematics from calcula...
4 comments
Read more

Rutherford Alpha Ray Scattering Experiment

Rutherford Alpha Ray Scattering Experiment Hey, Guys, most of you might have heard about the alpha ray scattering experiment and if you want to know in detail about Rutherford's model and the experiment he conducted, this is the right place for you... But first: Things You Must Know Some basic information that will help you understand rutherford experiment properly: Proton is a sub-atomic particle which is positively charged and has a mass of 1u. Alpha particles are helium atom with a charge of +2 as they have lost 2 electrons. Alpha particles have an atomic mass  of 4u. Gold is highly malleable and can be beaten into very thin sheets. Experiment Rutherford conducted his experiment in the following way: Rutherford took a very thin gold foil and bombarded it with high energy alpha particles. He placed a layer of zinc sulphide on the walls where the experiment was taking place because when alpha particles ...
10 comments
Read more

Pokemon Go 0.33.0

All Pokemon go fans get ready because again the latest version of Pokemon go is out. The Niantic has released a new version of Pokemon go i.e. 0.33.0.The size of the new version is 61.48MB.
8 comments
Read more