Combinations 7

The second important counting principle that you need to be aware of is the method of using combinations. In the case of counting using the method of permutations, you had considered the ‘order’ to be an important factor. Now, in the case of combinations, you need not take the order into account while finding the number of ways to arrange a group of objects. Let’s watch the following video as Amit explains the concept.

As explained in the video, when you just have to choose some objects from a larger set and the order is of no significance, then the rule of counting that you use is called combination. In the example mentioned in the video, you had to choose three bowlers from a set of four bowlers and obviously you did not need to order them here. Some other examples of combinations are as follows.

  • The number of ways in which you can pick three letters from the word ‘UPGRAD’.
  • The number of ways a team can win three matches in a league of five matches.
  • The number of ways in which you can choose 13 cards from a deck of 52 cards, and so on.

The formula for counting the number of ways to choose r objects out of a set of n objects is as follows:

Now, you might be wondering when to use permutations and when to use combinations. As mentioned in the video, one way to look at it is to see if the order matters or not. If it does, then use the permutations formula, and if does not, then use the one for combinations.


A helpful hint here would be to look for a keyword in the given scenario to know which method is needed. If the problem requires you to order/arrange a group of objects, then you would most probably use the method of permutations. Else, if you are told to pick/choose a group of objects, then more often than not you would be using the formula for combinations.

There are some other rules of counting as well. For example, recall that in the permutation case, we had assumed that no repetition was allowed in the order and, hence, we proceeded with the given formula. Now, what do we do if repetition is allowed in the process of counting the number of ways? You will get to know those types of examples in future sessions and will also learn how to find the answer in such cases. For the time being, you need to know only these two methods, i.e., permutation and combination.

Now, answer the following questions.

Now that you have learnt the two fundamental counting rules, we will go ahead and finally learn the basic definition of probability and its associated properties.

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