Permutations with Limited Repetitions

Duration: 9 min

This video lesson is available to enrolled students.

Return to /learn/WIPRO-PREPARATION/quantitative-aptitude/permutation-and-combination/permutations-with-without-repetition/asset-permutations-with-limited-repetitions after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. Quantitative Aptitude: Number System, Percentage, Profit and Loss, Ratio and Proportion (Ratios), Average, Time and Work, Speed Time and Distance, Simple Interest and Compound Interest, Mixture and Alligation, Data Interpretation, Permutation and Combination, Probability, Logarithm, Powers and Exponents (Surds and Indices), Age Problems, Divisibility Rules, Partnership, HCF LCM, Algebra, Pipe and Cistern
  2. Logical Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Analogy, Coding Decoding, Blood Relations, Directions (Direction Test), Syllogisms, Logical Sequence Of Words, Data Sufficiency, Seating Arrangements, Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Data Arrangement
  3. English Language: Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Vocabulary, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Active Passive Voice (Voice), Direct and Indirect Speech, Cloze Test (Cloze Passage), Tenses, Subject Verb Agreement (Verb Noun Agreement), Preposition, Articles, Conjunction, Adverb
  4. Written English Test: English Writing Ability
  5. Coding: Coding Questions by Yash Sir, C Programming by Yash Sir, Programming in C++, Java, Python for Placements by Yash Sir
  6. Communication Round: Communication Assessment
  7. DBMS (Technical Interview): Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Big Data Systems, NoSQL, Data Warehousing & Mining
  8. SQL (Technical Interview): SQL
  9. Operating Systems (Technical Interview): Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
  10. Computer Networks (Technical Interview): Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security, Mobile Technology, Cloud Computing and IoT, Cyber and Info Security
  11. OOPs (Technical Interview): Object Oriented Programming (OOPS)
  12. HR Interview: MR & HR Interview Preparation
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive lecture on permutations and combinations, specifically focusing on the case of limited repetition. The video begins with an introductory slide that visually distinguishes between permutations (where order matters) and combinations (where order does not matter), using examples like a combination lock and a pizza. The main content is a step-by-step derivation of the formula for arranging items with limited repetition. The instructor presents a problem: 'In how many ways can we arrange 5 items in 5 slots where 2 identical items are of type 1 and 3 identical items are of type 2?'. He then demonstrates the solution by first considering the total permutations of 5 distinct items (5!), and then dividing by the factorials of the counts of identical items (2! and 3!) to account for the indistinguishability. This leads to the general formula: N! / (N1! * N2! * ... * Nk!), where N is the total number of items and N1, N2, etc. are the counts of identical items. The video concludes with a summary of the general formula and a 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide that introduces the concepts of 'PERMUTATION' and 'COMBINATION' with illustrative images: a roulette table and dice for permutation, and a basket of fruit and a pizza for combination. This is followed by a slide titled 'Confused' which poses the question, 'Should I unlock with Permutation or Combination?'. The slide visually contrasts the two concepts with two locked doors, one labeled 'Permutation' and the other 'Combination', each with a detective character pondering the choice. The instructor, Yash Jain, is visible in a small window, introducing the topic. The slide also features the 'Knowledge Gate Educator' logo and branding.

  2. 2:00 – 5:00 02:00-05:00

    The video transitions to a new slide titled 'Permutation / Arrangement (Limited Repetition Case)'. The instructor presents a specific problem: 'In how many ways can we arrange 5 items in 5 slots where 2 identical items are of type 1 and 3 identical items are of type 2?'. He begins to solve this by writing the formula for permutations of 5 distinct items, which is 5!. He then explains that since the items are not all distinct, we must divide by the factorials of the counts of identical items to avoid overcounting. He writes the full formula as 5! / (2! * 3!). He also provides a visual analogy using 2 red balls and 3 black balls to illustrate the concept of identical items.

  3. 5:00 – 9:20 05:00-09:20

    The instructor continues to solve the problem, writing out the calculation: 5! / (2! * 3!) = 120 / (2 * 6) = 120 / 12 = 10. He then generalizes the formula for any number of items with limited repetition: N! / (N1! * N2! * ... * Nk!), where N is the total number of items and N1, N2, etc. are the counts of identical items. To reinforce the concept, he draws a table showing all 10 possible arrangements of the 5 items (r1, r2, b1, b2, b3), demonstrating that the order of the identical items (r1 and r2, or b1, b2, b3) does not create a new arrangement. The video concludes with a final slide summarizing the general formula and a 'Thanks for Watching' screen.

The video provides a clear and structured lesson on permutations with limited repetition. It effectively uses visual aids, such as the initial comparison of permutation and combination, and the problem-solving walkthrough with the 5-item arrangement, to explain the core concept. The instructor's methodical approach, from a specific example to a general formula, makes the topic accessible. The key takeaway is that when arranging items where some are identical, the total number of unique arrangements is found by dividing the total permutations of distinct items by the factorials of the counts of each set of identical items.

Loading lesson…