The topic of permutations and combinations holds significant importance in numerous entrance exams. This chapter plays a crucial role in various practical domains, such as economic statistics, probability theory, and voting theory. The fundamentals of permutations and combinations are nothing but a systematic and exhaustive enumeration or listing. 

Understanding of this topic requires basic aptitude for systematic counting. In this chapter we will study different techniques of counting. Permutation and combination is nothing but “counting without counting” or counting by using different models. For example, if we have to count total number of stars in the following grid:

* * * *

* * * *

* * * *

We do not need to count all the stars, as there are 3 rows and 4 columns, hence the total number of star points are 4×3 = 12. Though this is a very simple example to explain fundamental principles of counting, it gives the basic introduction to counting. Now consider another example, we have to find all three letter words which can be formed by using A, B, C without repetition, 

The diagram indicates that the first place can be filled in 3 different ways, when first place is filled second place can be filled in 2 different ways and then third place in 1 way. Hence total number of words is 3×2×1 = 6, the six words so formed are:

ABC, ACB, BAC, BCA, CAB and CBA