Permutations 7

Before we turn our focus to probability, it is important to understand some basic tools that form its essential building blocks. This session will require you to do a fair bit of calculations, so be prepared.

One of the key things that you need to master is the idea of the two major counting principles – permutations and combinations. Knowing these two concepts will enable you to calculate the probability for a given scenario or events that you are interested in. We will start by understanding the concept of ‘permutations’ in the upcoming video.


The 24 permutations represented for the four batsman in the video is incorrect, please find all the combinations below:

  • {Dhawan, Sharma, Kohli, Rahul}
  • {Dhawan, Sharma, Rahul, Kohli}
  • {Dhawan, Kohli, Sharma, Rahul}
  • {Dhawan, Kohli, Rahul, Sharma}
  • {Dhawan, Rahul, Sharma, Kohli}
  • {Dhawan, Rahul, Kohli, Sharma}

  • {Sharma, Dhawan, Kohli, Rahul}
  • {Sharma, Dhawan, Rahul, Kohli}
  • {Sharma, Rahul, Dhawan ,Kohli}
  • {Sharma, Rahul, Kohli, Dhawan}
  • {Sharma, Kohli, Dhawan, Rahul}
  • {Sharma, Kohli, Rahul, Dhawan}
  • {Kohli , Dhawan, Sharma, Rahul} 
  • {Kohli, Dhawan, Rahul, Sharma} 
  • {Kohli, Rahul, Dhawan ,Sharma}
  • {Kohli, Rahul, Sharma, Dhawan}  
  • {Kohli, Sharma, Rahul, Dhawan}
  • {Kohli, Sharma, Dhawan, Rahul}
  • {Rahul, Kohli , Dhawan, Sharma}
  • {Rahul, Kohli, Sharma, Dhawan}
  • {Rahul, Dhawan, Sharma, Kohli}
  • {Rahul, Dhawan, Kohli, Sharma}
  • {Rahul, Sharma, Dhawan, Kohli}
  • {Rahul, Sharma, Kohli, Dhawan}

To summarise the video, a permutation is a way of arranging a select group of objects in such a way that the order is of significance. As shown in the example, when you arrange the top order batsmen of a cricket team, you use permutation to find all the possible orders in which they can be arranged. The following list shows some other examples where permutation is used to count the number of ways in which a particular sequence of events can occur.

  • Finding all possible four-letter words that can be formed using the alphabets R, E, A and D.
  • Finding all possible ways in which the final league standings of the eight teams can be in an Indian Premier League (IPL) tournament.
  • Finding all possible ways that a group of 10 people can be seated in a row in a cinema hall, and so on.

Generally speaking, if there are n ‘objects’ that are to be arranged among r available ‘spaces’, then the number of ways in which this task can be completed is n!/(n-r)!. If there are n ‘spaces’ as well, then the number of ways would be just n!. Here n! (pronounced as n factorial) is simply the product of all the numbers from n till 1 and is given by the following formula:

Now, answer the following questions.

You have learnt to find the number of ways in which you can arrange items in an order using permutation. In the next segment on combinations, you will learn how to find the number of ways in which to choose a particular set of items.

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