Approaching Permutation and Combination for JEE Advanced:
Permutation and Combination or often referred as “PnC” among students is a topic which is all about logic and “counting”. This might sound weird but you’ll realise the same once you start solving problems of this topic. Unlike most of the other topics that you might have studied until now, PnC tests your ability to observe pattern, your mathematical reasoning and creativity. Here are some tips on how to approach this topic, particularly if you are preparing for JEE, Read on!
Understand the use of nPr and nCr :-
When you first start learning permutation and combination, nPr and nCr will be the two terms that you’ll learn and students generally use these two terms wrongly. So to start with refrain the usage of these two formulae and try to solve the problems without using them. Slowly you’ll understand the pattern and the need for these two terms in solving certain questions. It is only then that you’ll learn the usage of these terms perfectly.
Learn to observe Patterns :–
In a lot of questions of PnC you’ll be asked to solve a problem involving in general N objects. So to solve these type of problems it is wise that you first consider some value of N say 3 then solve the problem. Repeat this for other values of N and there are high chances that these values for different N’s will have a pattern hidden in there which you can use for solving in general for any N. This at first may seem time-consuming but once you have done enough practise it wont take much time to arrive at the solution.
Books to refer :-
Make sure that you are thorough with the theory of NCERT and solve all the questions of it. Then go through the book R.D. Sharma, PnC is explained very well in this book and there are ample of questions with crystal clear concepts. But again the choice of reference book depends on person to person, find the book that best suits you the best depending on how well you are clear with the concepts and the difficulty of the questions you require. Find a list of important books you MUST have for JEE in this article.
Practice is the key :-
In PnC one can form infinite number and type of questions and so one cannot be confident that they’ll be able to solve all questions of this topic. So to be able to solve maximum number of those you need to practise a lot, that’s the key. Solve variety of questions and first try to understand the question rather than jumping directly to the solution. In JEE questions from this topic won’t be too exaggerated and will test your basics. Make sure you practise the ball-box and other related problems, as many questions previously asked previously in JEE revolve around this concept. You can use Toppr’s huge question bank to practice to your heart’s content!
Performing at the real stage :-
In JEE, questions from this topic are intentionally added to reduce your time and it is not wise if you spend 5-10 minutes thinking of the solution only to realise that you won’t be able to solve it. While writing exam, what I will suggest is that you should proceed only if you are confident enough or if you feel that the question looks similar to ones you have solved before, if not so then you should give priority to other topics in which you are confident of scoring.
The aforementioned points should help you in your preparation and boost your confidence in PnC for JEE. Initially when you start off, questions from PnC might seem tricky and difficult but worry not, once you start solving and get the rhythm you’ll eventually realise that it was never a big deal. Getting proficient at anything is a function of time invested in it, so make sure you do devote sufficient time to this topic while practicing. Further, you can find the explanation of some of the basic concepts of permutation and combination here.
All the best!