RD Sharma Class 11 Chapter 16 Solutions (Permutations)
RD Sharma Solutions for Class 11 Maths Chapter 16 ‘Permutations’ is designed to help students strengthen their knowledge of the rules of permutations in mathematics, through numerous exercises. These questions enable you to prepare for any competitive exams. The exercises touch topics like the factorial, basic concepts of counting, permutations, permutations based on some conditions, and permutations of entities which are not all unique or distinct.
This chapter of RD Sharma Solutions has a total of 195 questions divided into 7 sections, which go over all the possible aspects of Permutations. The types of questions range from objective ones where you require choosing an answer from the given suitable answers to simple and complex problems in proving equations based on the different rules of permutations, fundamentals of factorial, and counting concepts and principles. This chapter will give you a solid base on the various concepts of Permutations.
Instasolv has provided RD Sharma Class 11 Solutions for Maths Chapter 16 ‘Permutations’ in a manner that is very easy to follow by breaking down complex problems into simple steps. These methods employed by experts at Instasolv will help you revise the entire syllabus and secure good marks. If you follow the tips and tricks of solving a problem here, it will let you do a much better time management. You should be able to deal with the stressful exam environment by practising with Instasolv.
Topics Covered in RD Sharma Solutions for Class 11 Maths Chapter 16 – Permutations
- Permutation – When you want to figure out which are the possible ways of arranging a single group of objects, we need to follow the law of permutation.
For example; letters ABC can be arranged in many ways like ACB, BAC, CBA, etc. In permutation the order of arrangement matters, so here ABC will be considered different from BAC since the order of the letters is changed in both the sequences. Permutation follows the following rule:
If there are n objects, where r objects are considered at a time, then the number of permutations would be = nPr
nPr = n (n-1) (n-2) (n-3)…..(n – r + 1) = n! / (n-r)!
- Permutations where the repetition of objects are allowed – If from a given lot of n objects we have to choose r of them, where an object can be repeated, then to get the number of permutations we use the below formula:
Number of permutations = n * n * n *…. (r times) = nr
- Permutations where the repetition of objects are not allowed – When repetitions are not allowed then the available choices would reduce. So if from a given lot of n objects we have to choose r of them, where an object cannot be repeated, then to get the number of permutations we use the below formula (also called the factorial) :
Number of permutations = n! / (n-r)!
- Permutation of non-distinct objects – If in a set of n objects, there are duplicate objects then we need to use a different formula. Say for example there is a sheet of stickers which has 10 stickers. 3 of them are stars, 4 are numbers, and 3 are moons then the number of ways to arrange them would be defined by the below formula:
Number of permutations = n! / (a! * b! * c!…z!)
Here n = total number of objects
a, b, c = these are the number of identical objects, as in the above example it would be: 10! / ( 3! * 4! * 3!)
- Basics of counting principle: The counting principle or the counting rule is how you find out the number of outcomes in a problem of probability. You arrive at the total number of outcomes for a given number of events by multiplying them together. Below is the formula for this:
For an event “x” and another event “y”, the sum total of different outcomes for these 2 events = x * y
- Factorials – A factorial is represented by an exclamation mark (!) and for any number “x”, its factorial is the product of all the whole numbers starting from 1 till “x”. The criterion here is that “x” is always a positive number.
Example: – 4! = 4 * 3 * 2 * 1.
Here 0 is considered a special case and we say that 0! = 1. By saying this we claim that there are no numbers whose product is 1.
- Permutations with special conditions and restrictions: There are some special arrangements of objects which can fall under the below categories:
- If there are n objects and we take r objects at a time where a certain object is always included then:
Number of Permutations = r * (n−1) * Pr−1
- If there are n objects and we take r objects at a time where a certain object is never included then:
Number of Permutations = (n−1) * Pr
- If there are n objects and we take r objects at a time where 2 objects are always placed together then:
Number of Permutations = 2! * (r−1) * (n−2) * Pr−2
Discussion of Exercises of RD Sharma Solutions for Class 11 Maths Chapter 16
- The questions in the first exercise of RD Sharma Class 11 Maths Chapter 16 are based on factorial formulas with varied ways of proving formulas and applying them. It has 19 questions.
- The second set of exercises gives you ample practice on the different laws of permutation. It has 48 questions.
- The third set is again based on permutation but they deal with all the special conditions that may apply while coming up with the permutations total. It has 35 questions.
- The fourth set of exercises are again on permutations and how they can be applied in different conditions. It has 23 questions.
- The fifth set has slightly complex questions on the concepts of permutations which will make you apply the learnings of factorial and permutations together to solve them. It has 36 questions.
- The sixth set has very short answers which have a mix of all the concepts; factorial, permutations, and counting principle. It has 12 questions.
- The MCQ section is an objective type where you are given a problem with 4 possible answers and you have to select one based on your derivations. It has 22 questions.
- The questions by RD Sharma are oriented towards making you score good grades in CBSE exam as well as prepare you for any of the engineering or medical exams you want to take.
Benefits of RD Sharma Solutions for Class 11 Maths Chapter 16 by Instasolv
Instasolv has shown how even a complex permutation-based exercise can be solved in simple ways through RD Sharma Solutions for Class 11 Maths Chapter 16 ‘Permutations’. The free RD Sharma solutions are a very systematic approach towards solving mathematical equations. It will make time-management a breeze for you and will prepare you well for CBSE, JEE, NEET, BITSAT and other tests.