# Important Points on Combinations

In  2022, the JEE Main first session exam will be conducted via online mode by the NTA in the month of June. As per the notification of the NTA, there will be only two sessions this year. Due to the pandemic situation, there were four sessions in 2020 and 2021. Through proper planning,  learning and hardwork, one can easily crack the JEE Main exam. The registration for the first session of the JEE Main 2022 has started on March 1, 2022. The exam will be conducted in 13 languages, and students can choose the language while filling out the application form.

The duration of the test is 3 hours.

Permutation and combination is an important topic as far as the JEE Main exam is concerned. In mathematics, permutation is a technique that calculates the number of possible arrangements in a set when the order of the arrangements matters. When the order of arrangement does not matter, it is a combination. We can select items in any order, in combinations. Students get confused with permutation and combination. There are two types of permutations. They are permutations with repetition and permutations without repetition. The combination is also of two types, i.e., with repetition and without repetition.

## Formula

The number of ways of selecting r objects out of n objects irrespective of order is given by,

nCr = n!/r!(n-r)!. Here ! denotes factorial.

The permutation is given by nPr = n!/(n-r)!

Note: nCn = 1

nC0 = 1

Let us look at one example of a combination.

Example 1: Find the number of ways to put 9 letters in respective envelopes so that exactly 4 go into the correct address?

Solution:

Number of selecting 4 correct envelopes = 9C4 = 126

Derangement of remaining 5 envelopes is D5 = 44.

Hence the total number of ways of arrangement = 44×126 = 5544.

### Problems on Probability

The outcome of an experiment can be explained using probability. We can use probability to predict the occurrence of an event. We calculate the probability of an event by dividing the number of favourable outcomes by the total number of outcomes of an event. Probability problems have great importance for the JEE exams. Students are advised to thoroughly learn these problems so that they can easily crack them. Probability is an easy topic if learnt properly. Cracking the JEE main exam is not an easy task. Students should be careful while selecting the study materials since a large number of study materials are available in the market. So, they are recommended to take advice from their teachers before selecting them. They can also make use of the internet wisely for learning purposes. Many websites provide free pdfs, JEE revision notes etc. Previous years’ question papers solving videos are also available on different websites.

Students are advised to attempt mock tests, which are available online. This will help them to be familiar with the exam scenario. It will increase their confidence and problem-solving skills, and thus, they can be stress-free during the actual exam. Log on to BYJU’S to learn previous years’ solved questions of probability.

##### By Flavia Calina
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