Higher Algebra Hall & Knight Permutations & Combinations (Chapter 11) Solutions

Hall & Knight Higher Algebra Solutions for Chapter 11 ‘Permutations and Combinations’ comprises of all the essential topics that will help you in preparing for competitive exams like IIT JEE and NEET. Our solutions for Permutations and Combinations will help in forming a stronger command of the derivation of permutations, determining combinations and solving problems based on different situations. You will also learn about the concepts of permutation formula and selection of terms. The solutions also cover vital ideas regarding the arrangement of alphabets, analyzing conditions and dealing with application-based problems. We have included detailed theoretical explanations along with solved exercises of the chapter to help you form a better understanding of the topics. 

Higher Algebra by Hall and Knight ‘Permutations and Combinations’ solutions include 2 exercises which have 67 questions in total. These exercise questions help you in getting geared up to solve all the possible kinds of questions related to Permutations and Combinations in exams. Once you solve these questions you will learn to solve problems which deal with combinations, arrangements, dissimilar quantities and distribution of terms. We have based our solutions on the latest JEE exam pattern to help you prepare for such competitive exams easily. 

Elementary Algebra and Higher Algebra by Hall & Knight solutions Permutations and Combinations have been prepared to make sure that your time is invested in brushing up your fundamentals of the chapter. Also, you will be able to solve the higher-order thinking questions of the chapter easily. We ensure that all your concepts picked from the chapter are strengthened and your preparation is well managed rather than wasting time in the struggles of reaching out to different resources of learning. 

Important Topics for Hall and Knight Higher Algebra Solutions Chapter 11: Permutations and Combinations


In this chapter, you will be introduced to the concept of Permutation. You will learn that each and every arrangement which can be made by taking some or all of the provided number of things are termed as permutation. Taking a simple example,

Consider four alphabets a, b, c and d 

Now, these four alphabets can be arranged 12 times in order to form different combinations. These 12 arrangements are ab, ac, ad, bc, bd, cd, ba, ca, da, db and dc.

Here as you can see all the arrangements are unique and no repetition can be witnessed. Also, these are the maximum possible number of arrangements which can be done from the provided set of information. 

Circle Permutation 

In this chapter, you will also learn about circular permutation. This is used when the objects can be arranged in the form of a loop. You will learn about the rules of selection of objects and their particular formation in the chapter.


The groups or selections which are made to form the arrangements are termed as combinations. Taking the same example of a, b, c and d.

The number of combinations we can make from these four alphabets by taking only two alphabets at a time is 6 i.e. ab, ac, ad, bc, bd and cd.

Exercise Discussion of Higher Algebra by Hall and Knight Chapter 11: Permutations and Combinations

Example XI a 

  • This exercise has a total of 34 questions. 
  • It majorly comprises of word problems which are application based and analytical questions. 
  • There are questions where you are required to find the number of ways in which a consonant and a vowel can be chosen out of the given letters or the arrangements that can be made from a given set of alphabets.
  • There are questions where you are required to use your reasoning skills in order to find the number of combination of things or the ways in which a party can be selected from the given digits. 
  • There are problems revolving around boat questions, number of people, number of days and alphabets.
  • The exercise also includes questions where you are required to prove the given set of permutations with respect to the conditions provided in the question. 

Example XI b 

  • This exercise comprises of a total of 33 questions. 
  • It also includes questions related to alphabets and begins with a question where you are required to find the number of arrangements which can be made by the letters present in the provided three words
  • Then there are questions related to billiard balls, where the number of different colour balls and the total number of balls is provided to you and you are required to find the number of ways in which it can be arranged.
  • The exercise also has logic-based questions like problems with different number of ways through which a person drives to his/ her destination 
  • The exercise also has problems related to digits and sides of shapes like triangle, quindecagon. 
  • Overall the exercise has different kinds of word problems, most of which have been already introduced as solved examples in the course of explanation of the chapter. 

Why Use Hall and Knight Higher Algebra Solutions Chapter 11: Permutations and Combinations by Instasolv?

  • Our team of subject specialists has ensured that all the Hall & Knight Algebra Book solutions are framed to address questions with a step by step manner.
  • We have kept the language to be easy to understand and student-friendly. 
  • In our solutions for Higher Algebra By H.S. Hall and S.R. Knight Permutations and Combinations, we have ensured that no corner of the chapter is left untouched and every question is carefully dealt with. 
  • We have ensured that all the essential concepts and fundamentals are presented in a compiled format to simplify the learning process. 
  • All our solutions follow the latest guidelines of competitive exams for Class 12. 
  • The most remarkable point about our Hall and Knight Higher Algebra Solutions is that you can access them to prepare for Class 12 board exams as well and revise the fundamentals of the chapter.