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

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

Levitation 2

LEVITATION II To be completely honest I was going to start this with a pun. I did think of one but it doesn’t float… I am sorry I just had to. Anyway, this is the second part to the article on super cool ways of making things levitate. Go check the first part out if you haven’t already. Actually, the first part may have become repulsive with all the magnets and stuff, but I promise this will be more attractive. Get it? No? I’ll stop now. I am just going to jump straight into it. 1.    Electrostatic Levitation I know you are probably sick and tired of magnets but they are the best way you know… This method is somewhat similar. You remember that cool science experiment you did with two straws attracting or repulsing each other based on their charge? So basically using the same principle we can make a charged object levitate. But before you try it, let me tell you it won’t be easy. Even impossible according to our Mr. Earnshaw. He even made a law (th...
4 comments
Read more

Want To Make Your Smart Phone Really Smart

Nowadays everyone uses smartphones. But the question arises that are they using it smartly? Smartphones are the shortcut to various needs which makes it smart. But till what limit? Therefore smartphone can be used for everything and to achieve this you just have to read the following article. Movies Everybody watches movies but to open PC and then download is time-consuming.Thus Showbox is an app which downloads movies with one touch and even TV shows like ‘Friends’, ‘The Big Bang Theory’, Etc.
Post a Comment
Read more

Stains And Dyes

STAINS AND DYES Stains and dyes are used to great lengths in microbiology to highlight certain parts or organelles of cells when put under the microscope. They can also be used to classify the various parts of the cells and different cell groups in a tissue. Stains can be used on their own as well as mixed with other stains and dyes. In fact, the process of using multiple stains to highlight important parts of an already stained cell is called counterstaining. You may have used safranine while preparing a temporary mount of leaf peel to observe stomata. That is an example of a stain. When it comes to the process of applying stains, there are broadly two different classifications: IN VIVO staining and IN VITRO staining. As the name suggests, IN VIVO staining is practised on live tissue. It helps us observe the chemical reactions taking place within a living cell. Stains are used here to highlight the chemicals and chemical reactions taking place. IN VITRO staining is pract...
Post a Comment
Read more

Piezoelectric Crystal

Piezoelectric Crystal {literally_pressing electricity} Ever wondered what it might be like to live in dark or sleep in a hot summer day without an AC ? Absurd, isn't it ? But with the rate at which we are using our resources, it may not be long before it actually happens. Scientist across the globe are searching for new resources, stocks and technology to prevent the near, unpleasant future of current and the next gen. One of these, an unexploited tech is that of Piezoelectricity. Piezoelectricity is an ability of some special materials (like crystals of quartz, ceramics of lithium niobite, gallium arsenide, zinc oxide) to trigger an electric charge when supposed to mechanical stress. These materials are available in basic instruments that we use in our daily life like microphones, quartz watch, gramophones. All these materials are run by the piezoelectric current. But how does it work? When you apply force (mechanical force) on it, an electric potential, on eit...
1 comment
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

High School Pedia

It is an initiative by some students to spread the light of knowledge to everyone and everywhere. It was started in the year 2015 and has grown rapidly in the past few months. By the means of this website, we try to provide information on every topic that we can reach up to. You can find different articles on this website. All these articles are written in simple language so that everyone can understand it and learn from it. We at High School Pedia believe in creative learning and this is the reason why we add our own edited graphical representations in every article. Once a very learned man said, “Knowledge increases by not keeping it to yourself but by sharing it with others”. And we follow the same motto “Share to Learn”. The team of High School Pedia tries its best to provide you with the best and original content. Unlike many other websites, High School Pedia is famous for its original and inspiring content.
2 comments
Read more