This chapter of class 11 maths explains the concepts of Permutations and Combinations. This will increase the level of understanding about the concept of arrangement and selection of a group of objects in different ways. This chapter will make students understand these concepts and theorems in an easy way. Permutation and Combination formula is very important for the students.

The concepts of permutations and combinations are traced back to the advent of Jainism or even earlier. The credit goes to the Jains for treating it as an independent subject in mathematics.

In this chapter, students will learn about Permutations and Combinations in detail. These concepts of Permutations and Combinations are all about the methods the counting, arrangement, and selection of elements in some collections. Permutation and combination are all about counting and arrangements made for a certain group of data. Concepts with a diverse set of solved questions along with formulas will help to make a strong understanding. Moreover, practice questions based on these concepts will improve the skills of the students for data handling and arrangements.

Subtopics covered in this chapter are the Fundamental Principle of Counting, Permutations, Permutations when all the objects are distinct, Factorial notation, Derivation of the formula for n_{P_r}, Permutations while all the objects are not distinct objects and Combinations.

The student will study the fundamental principle of counting, Factorial (n!), Permutations and combinations. Also, they will learn the derivation of the Formulae for n_{P_r}.and n_{C_r}. Firstly, they will learn some basic counting techniques which will be the most fundamental to the learning of these techniques. Fundamental Principle of Counting states that, if an event can occur in p different ways, and further another event can occur in q different ways, then the total number of occurrence of the events will be p \times q.

The permutation is the process for arranging in various possible orders and arrangements. It is the arrangement in a definite order of a number of objects while taking some or all at a time. Permutations occur, in more or less different ways, in almost every area of mathematics. They often arise with different orderings on certain finite sets are considered.

Combinations are also an interesting topic. It is based on the selection of some objects to make the group without considering ordering. Such selection is the combination. In a combination of objects, we do not bother about the order. The combination is useful as a way of selecting items from a collection. In these cases, it is possible to count the number of such combinations. The combination will refer to the combination of n things taken r at a time without their repetition. To refer to combinations in which repetition is allowed, the terms r-selection or r-combination are used with repetition.

The difference between the combinations and permutations is the ordering. With permutations, we bother about the order of the elements, but with combinations, we need not. The formula for the permutations is similar to the combinations of the formula, except we need not divide out the permutations by the term r!