Skip to main content

Combination

Hey guys, in my last article I told you about permutations and the difference between both permutation and combinations. In this article we are gonna learn more about Combinations and uses of these arrangements.
Link for my last article : Combinations and Permutations


Combinations
Now we noticed that in Permutation we check every small detail and everything is in order but Combinations is completely opposite to it. In Combinations we are free to choose and we have no restriction for orders too. So Combinations and Permutations are like College and School. Now you would be able understand the difference properly. After the difference comes your actual meaning of this term Combinations.



Now let us take the same example as before. But this time I am a bit kanjoos(stingy), I don't want to give three different cars but three same bikes. So how many ways are there in which i can give these 3 bikes to 9 friends?? Eventually this time the order does not matter. Giving a bike to Arya then Bhavesh and then Chirayu is same as giving a bike to Chirayu then Bhavesh and at last to Arya. It is same in any order as all of them are unhappy.

So now how many ways are there in which I can give these 3 bikes to them. In the first I have 3 options, then for the second 2 options are left and at the last only option. So the total is 3*2*1=6.

By this we could conclude that if you have "x" number of people and want to know how many possible ways are their for them then it is " x! ". You notice that these 6 ways are just useless for combinations as there is no specific order required in combinations. Now we know P(n,r) and also all the useless possibilities, so time to find combinations.

If we want to find out all the possible combinations then we just find all the permutations and divide it by all the useless possibilities. In this example we get 504 permutations ( from my last article) and we divide it by 6 useless ways and in the end we get 504/6 = 84 combinationsin all for the 9 friends.

So the Formula we get for Combinations is 
                                                  C (n,r) = P(n,r) / r!

Which in the universal method can be written as
                                                       
                                              C (n,r) = n! / (n-r)! r!






Common Life Examples for Permutation and Combination

  1. Combo Lock Designers :
       These are the people who design number locks for your cars, bikes and houses. They use the theory of          Permutation to find out the non used patterns and provide you with a safe number pattern.

 

      2.  Seating Arrangements :
      These days managing a crowd for an large event has become simpler with the use of Combinations and   
      Permutations. You can now get the accurate number of possibilities rather than just confusing yourself up       with some guessing game.


               
  
      3. Selecting A Phone Number :
     
      Every teen wants a phone and a phone number that he can share with everyone. And that is the time 
      when this concept helps. For a phone number the first four digits are fixed and you can only customize 
      the last 6 digits. With the help of Combinations you know the exact ways and you could find the best             possible number.
         
         


    I hope you guys have understood the concept of Permutation and Combinations. If the article was interesting and you loved it then do share it with your friends, family, teachers,neighbors and everyone.
If you want any other math topic to be published then do write it in the comments section,. Thanks for reading this article and spending your valuable time with us.


You may also like these articles from High School Pedia :

Comments

Popular Posts

Isotopes, Isobars and Isotones

Isotopes These are elements which have the same atomic number but different atomic mass . They have the same atomic number because the number of protons that are inside their nuclei remains the same. But, they have different atomic mass because the number of neutrons that are also inside their nuclei is different. As the number of protons inside nuclei remains same, therefore the overall charge of the elements also remains same as in isotopes: no of protons = no of electrons . Hence, as isotopes overall charge remains neutral, therefore their chemical properties will also remain identical.   Therefore, Isotopes are chemically same but physically different.

Anode Ray Experiment

→Anode ray experiment was conducted by E Goldstein. →These rays are also known as canal rays. →This experiment helped in the discovery of the proton. Apparatus Used A discharge tube  was taken in which there were 2 electrodes i.e. Anode(+ve) and the cathode (-ve). The tube was filled with an inert gas. A perforated or porous cathode was used. A layer of zinc sulphide was placed at the back of the cathode. There was a vacuum pump in the tube. High voltage (5000v-10000v) was allowed to flow through the system. It was observed that when the gas was at 1atm(atmospheric pressure ) no change was seen in the tube.  When the   pressure   was decreased inside the tube, a glow could be seen at the back side of the cathode.

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."

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 strike zinc sulphide layer, it results i

Cathode Ray Experiment

This experiment was conducted by J.J. Thomson (Sir Joseph John Thomson) in the year 1897. This experiment proved that atom is made up of fundamental particles which are much smaller than the smallest atom 'hydrogen' This experiment helped to discover electron. According to J.J. Thomson, the cathode rays consisted of very light, small and negatively charged particles. He named the particles "corpuscles" which were later known as electrons

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.

Lets talk STARS

Hey guys, have you ever spent any of your nights at the uncovered top floor or backyard of your house. If you have then this article will help know about all the things, you just observed out there in the space or even if you did not have this article will help you observe and understand all the miracles that happen in that huge space above us. In this one, we will talk about STARS- STARS There are about 6k-10k stars that a person with a normal eyesight can observe in that huge space.(well that number varies according to your eyesight) You might have observed or will observe that the stars in the space are not all the same in brightness and color. Well, the brightness of a star depends on the combination of 2 reasons.   The ACTUAL BRIGHTNESS -   Actual brightness of a star refers to the magnitude of real brightness that, that particular star have.You can think of that as energy.Different stars have different levels of energy(brightness).The star with more energy w