RD Sharma Class 11 Maths Solutions Chapter 16 - Permutations

RD Sharma Solutions for Class 11 Maths Chapter 16 - Free PDF Download

Permutations and combinations are the different ways in which objects from a set may be selected to form subsets, usually without a substitution. When the order of selection is a factor, this selection of subsets is called a permutation, we use combination when order is not a factor. Permutation and Combination class 11 RD Sharma is one of the most important chapters in board exams as well as in competitive exams. The RD Sharma Class 11 Chapter 16 Solutions are prepared according to the NCERT curriculum by experts.

All solutions are explained clearly in a step-by-step manner to provide a unique learning experience to students. The RD Sharma Solutions of Class 11 Maths Chapter 16 also have a lot of exercise and practice problems so that students will have enough practice of the subject before their exams. Students can download a free PDF of Permutation and Combination class 11 RD Sharma solutions free of cost.

Chapter 16 - Permutations

Students can use these permutations to help them get good grades on their board exams. From a set of 'n' objects, the number of possible 'r' object pairings. As a result, permutations are employed for lists (where the order is important) and combinations for groups (where the order is irrelevant). This chapter will introduce the terms factorial and factorial notation. The RD Sharma Solutions module uses a variety of shortcut hints and pictures to explain all of the exercise issues in plain English.

There are five exercises in Permutations, and the RD Sharma Solutions provide precise answers to the questions in each one. Vedantu's specialists have broken down tough problems into easy steps that students can solve quickly and accurately. RD Sharma Class 11 Maths Solutions can assist students in gaining a thorough understanding of the topic. As a result, students should practice the solutions by obtaining the pdf from the links provided below. Let's take a closer look at the principles covered in this chapter.

The factorial.
Fundamental principles of counting.
Permutations.
Permutations under certain conditions.
Permutations of objects are not all distinct.

What is Permutation?

A permutation is an arrangement of a number of objects in a specific order, taken one at a time or all at once. Consider the following ten numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. P(10,4) = 5040 is the number of different 4-digit-PINs that may be constructed using these 10 digits. This is a simple permutation example. Permutations of four numbers drawn from a set of ten numbers equal to the factorial of ten divided by the factorial of the difference between ten and four. The permutations are simple to calculate.

FAQs on RD Sharma Class 11 Maths Solutions Chapter 16 - Permutations

1. How do the Vedantu solutions for RD Sharma Class 11 Maths Chapter 16 help in solving specific exercise problems?

Vedantu's RD Sharma solutions for Chapter 16 provide a detailed, step-by-step methodology for every question in the exercises. For each problem, the solutions help you:

Identify whether the problem involves a permutation or combination.
Determine the correct values for 'n' (total items) and 'r' (items to be arranged).
Apply the appropriate permutation formula, such as nPr = n! / (n-r)!, with clear calculations.
Understand the logic behind permutations with specific conditions, ensuring you can tackle any problem in the textbook.

2. What is the main difference between permutations and combinations that RD Sharma Class 11 solutions clarify?

The key difference, which is fundamental to Chapter 16, is that order matters in permutations but does not matter in combinations. For example, arranging the letters A, B, C is a permutation (ABC is different from BAC), while selecting a committee of 2 people from a group of 3 is a combination (Person 1 and Person 2 is the same committee as Person 2 and Person 1). The RD Sharma solutions repeatedly highlight this distinction when solving problems.

3. Why is it crucial to master the concept of 'factorial' (n!) before attempting permutation problems in RD Sharma?

The concept of factorial is the mathematical foundation of permutations. The primary formula for permutations, nPr, is calculated using factorials. Without a clear understanding of what a factorial is and how to calculate it, you cannot solve permutation problems correctly. The step-by-step solutions in RD Sharma assume you understand this basic principle and apply it directly in the calculations for each arrangement.

4. How do the RD Sharma solutions for Chapter 16 explain the method for solving permutations where some objects are not distinct?

For problems where objects are repeated (e.g., arranging the letters in the word 'SUCCESS'), the solutions use a specific formula. The method involves dividing the factorial of the total number of objects by the factorial of the count of each repeating object. The formula is: n! / (p1! * p2! * ...). The solutions break this down by first identifying the repeating objects, counting their frequencies (p1, p2, etc.), and then substituting these values into the formula for a clear answer.

5. What is a common mistake students make when solving permutation problems, and how do these solutions help avoid it?

A very common mistake is misinterpreting the constraints of a problem, such as whether repetition is allowed or if certain items must be placed together. The RD Sharma solutions on Vedantu help prevent this by carefully breaking down the problem statement first. They explicitly state the conditions and show why a particular formula or approach is used, building a strong logical foundation and reducing the chances of careless errors.

6. How do the solutions demonstrate the real-world application of permutations using problems from the textbook?

The RD Sharma textbook includes many word problems based on real-world scenarios. The solutions demonstrate how to translate these scenarios into mathematical problems. For instance, they show how concepts of arranging people in a line, assigning positions, creating passwords, or ordering digits on a number plate are all practical examples of permutations where the order of arrangement is critical.

7. Are the methods for complex topics like 'circular permutations' simplified in the Chapter 16 solutions?

Yes, for more advanced topics like circular permutations, the solutions provide a simplified approach. They first explain the core concept that in a circular arrangement, the relative position matters, not the absolute position. They then clearly apply the formula for circular permutations, which is (n-1)!, and walk through the textbook problems to show how it differs from arranging items in a linear row.

8. Beyond just getting the correct answer, what problem-solving skills can be developed by following the RD Sharma Chapter 16 solutions?

By consistently using these solutions, you develop crucial problem-solving skills beyond simple calculation. You learn to:

Deconstruct complex word problems into manageable parts.
Identify the key constraints and conditions in any arrangement scenario.
Select the correct mathematical tool or formula for a given situation.
Structure your answer in a logical, step-by-step format, which is essential for scoring well in exams.