The RD Sharma Solutions for Class 11 Maths Chapter 16: Permutations are essential resources for students aiming to excel in their final exams. This chapter introduces the concept of selecting and arranging ‘r’ items from a group of ‘n’ distinct objects — a concept known as permutations, where the order of selection is important. In contrast, combinations are used when the order does not matter.
In this chapter, students learn foundational concepts such as factorials, counting principles, and different types of permutations, including those under special conditions and involving non-distinct objects. The RD Sharma solutions make use of illustrative examples and shortcut techniques to help students grasp these concepts more effectively and solve problems accurately.
RD Sharma Solutions Class 11 Chapter 16 – Overview
This chapter is structured into five exercises, each focusing on a specific aspect of permutations. Topics include:
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Factorials and their notation
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Fundamental principles of counting
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Basic permutations and their applications
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Permutations with specific conditions
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Permutations involving identical items
Each question in these exercises is answered in a step-by-step manner, making it easier for students to understand even the trickiest problems. The detailed breakdown of concepts also helps in improving analytical thinking and problem-solving speed — crucial for competitive exams.
RD Sharma Solutions for Class 11 Maths Permutations Question with solutions
1st digit: 5 choices
2nd digit: 4 choices
3rd digit: 3 choices
Total = 5 × 4 × 3 = 60
Total = 5! / (2! × 2!) = 120 / 4 = 30
Choose and arrange 4 = 8P4 = 8! / 4! = 1680
Total = 6! / (3! × 2!) = 720 / 12 = 60
Remaining letters = 4! = 24
Total = 2 × 24 = 48
Ways = 4! × 2! = 24 × 2 = 48
Remaining = 4 digits → 4 × 3 × 2 = 96
Total = 7! / (3! × 2!) = 5040 / 12 = 420
Circular permutations = 3!
Internal arrangements = 2!
Total = 6 × 2 = 12
Total = 5! / 2! = 60
Second = 8, Third = 7
Total = 9 × 8 × 7 = 504
Together = (5−1)! × 2! = 24 × 2 = 48
Not together = 120 − 48 = 72
Letters: III, N(2), F, T, Y
Total = 6! / 2! = 360
Total = 10! / (3! × 3! × 2!) = 3628800 / 72 = 50400
Each pattern = 3! × 3! = 36
Total = 36 + 36 = 72
Remaining = 5! = 120
Total = 3 × 120 = 360
Together = 7! × 2! = 10080
Not together = 40320 − 10080 = 30240
Why Use These Solutions?
These solutions have been crafted by subject experts to ensure accuracy and clarity. Difficult problems are simplified into manageable steps, allowing students to develop a strong conceptual foundation in permutations. Whether you’re preparing for school exams or entrance tests, these solutions are a reliable guide to mastering the topic.
Students are encouraged to download the PDF version of these solutions for offline practice and revision.
Frequently Asked Questions
Chapter 16 of RD Sharma Class 11 Maths focuses on permutations, which deal with arranging a group of items in a specific order. The order of objects is important in permutations, and the chapter covers different types, such as permutations of distinct objects, identical objects, and circular permutations.
Permutations involve arrangements where order matters.
Combinations are selections where order does not matter.
For example:
Arranging ABC and CBA are different permutations, but the same combination.
Factorial notation and simplification
Fundamental principle of counting
Permutations of distinct objects
Permutations with identical items
Circular permutations
Restricted permutations (e.g., items together or not together)
Understand the situation – is order important?
Identify if repetition is allowed or not
Use factorial identities to simplify expressions
Break down constraints like "together", "not together", or fixed positions
Practice word problems like seating, forming numbers/words, etc.
The following topics from the chapter are crucial:
Permutations of n different things taken r at a time
Permutations when some objects are identical
Restricted permutations (e.g., two people must sit together)
Permutations in circular arrangements
Try to solve all examples and miscellaneous exercises from RD Sharma for complete mastery.
Yes.
Permutations (along with combinations) are important in JEE, NDA, CUET, and other entrance exams. Mastery of this chapter builds a strong base for probability and advanced counting principles used later in Class 11 and 12.
Permutations are used in:
Seating arrangements (e.g., weddings, boards)
Forming passwords or PINs
Scheduling tasks or events
Genetics and bioinformatics
Computer algorithms that generate sequences