Demo: Permutation & Combination (Quick Revision & Practice Questions)

Duration: 1 hr 11 min

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Inside: a video lesson and guided study material.

Module outline

  1. Paper - 1 | Unit - 1 | Teaching Aptitude: Concept and Objectives of Teaching / शिक्षण की अवधारणा एवं उद्देश्य, Levels of Teaching / शिक्षण के स्तर, Learner's Characteristics / शिक्षार्थी की विशेषताएँ, Learning: Nature and Theories / अधिगम: प्रकृति एवं सिद्धांत, Cognition, Memory and Metacognition / संज्ञान, स्मृति एवं अधिसंज्ञान, Factors Affecting Teaching / शिक्षण को प्रभावित करने वाले कारक, Effective Teaching and the Teacher / प्रभावी शिक्षण एवं शिक्षक, Instructional Objectives and Lesson Planning / अनुदेशनात्मक उद्देश्य एवं पाठ नियोजन, Methods of Teaching / शिक्षण विधियाँ, Offline and Online Teaching Methods / ऑफ़लाइन एवं ऑनलाइन शिक्षण विधियाँ, Teaching Support System / शिक्षण सहायक प्रणाली, Evaluation Systems / मूल्यांकन प्रणाली, Biological Basis of Emotion / संवेग का जैविक आधार, Central and Peripheral Nervous Systems / केन्द्रीय और परिधीय तंत्रिका तंत्र
  2. Paper - 1 | Unit - 2 | Research Aptitude: Research: Meaning, Features and Scientific Method / अनुसंधान: अर्थ, लक्षण व वैज्ञानिक विधि, Research Paradigms and Approaches / अनुसंधान के प्रतिमान एवं उपागम, Types of Research / अनुसंधान के प्रकार, Variables and Measurement / चर एवं मापन, Methods of Research / अनुसंधान की विधियाँ, Steps of Research / अनुसंधान के चरण, Sampling / प्रतिचयन, Tools and Methods of Data Collection / आँकड़ा संग्रह के उपकरण एवं विधियाँ, Data Analysis and Statistics in Research / आँकड़ा विश्लेषण एवं शोध सांख्यिकी, Thesis and Article Writing / शोध-प्रबंध एवं लेख लेखन, Application of ICT in Research / अनुसंधान में ICT का अनुप्रयोग, Research Ethics / शोध नैतिकता
  3. Paper - 1 | Unit - 3 | Comprehension: Literal Comprehension, Vocabulary and Language in Context, Inferential Comprehension, Critical Comprehension, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions)
  4. Paper - 1 | Unit - 4 | Communication: Communication: Meaning, Nature and Process / संचार: अर्थ, प्रकृति एवं प्रक्रिया, Types and Levels of Communication / संचार के प्रकार एवं स्तर, Verbal and Non-verbal Communication / मौखिक एवं अमौखिक संचार, Semiotics and Meaning / संकेत विज्ञान एवं अर्थ, Models and Theories of Communication / संचार के मॉडल एवं सिद्धांत, Effective Communication / प्रभावी संचार, Barriers to Communication / संचार की बाधाएँ, Classroom Communication / कक्षा संचार, Mass Media: Types and Evolution / जनसंचार माध्यम: प्रकार एवं विकास, Mass Media and Society / जनसंचार एवं समाज, Digital and New Media / डिजिटल एवं नव माध्यम, General Awareness (Legacy Paper 1) / सामान्य जागरूकता (पुराना पेपर 1)
  5. Paper - 1 | Unit - 5 | Mathematical Reasoning and Aptitude: Number System and Simplification / संख्या पद्धति एवं सरलीकरण, Algebra and Ages / बीजगणित एवं आयु, Percentage / प्रतिशतता, Ratio, Proportion, Partnership and Mixtures / अनुपात, समानुपात, साझेदारी एवं मिश्रण, Averages / औसत, Profit, Loss and Discount / लाभ, हानि एवं बट्टा, Simple and Compound Interest / साधारण एवं चक्रवृद्धि ब्याज, Time and Work / समय एवं कार्य, Speed, Time and Distance / चाल, समय एवं दूरी, Mensuration and Geometry / क्षेत्रमिति एवं ज्यामिति, Series / श्रेणी, Coding-Decoding / कूटलेखन-कूटवाचन, Relationships, Directions and Ranking / संबंध, दिशा एवं क्रम, Arrangements, Puzzles, Clock and Calendar / व्यवस्था, पहेलियाँ, घड़ी एवं कैलेंडर, Mathematical Foundations, जीवनी, Philosophy of the Constitution / संविधान का दर्शन, Analysis, Indian Polity and Governance (Legacy Unit 10) / भारतीय राजव्यवस्था और शासन (पुराना यूनिट 10)
  6. Paper - 1 | Unit - 6 | Logical Reasoning: Structure of Arguments / युक्ति की संरचना, Terms, Definitions and Uses of Language / पद, परिभाषा एवं भाषा के उपयोग, Categorical Propositions / निरुपाधिक प्रतिज्ञप्तियाँ, Categorical Syllogism / निरुपाधिक न्यायवाक्य, Venn Diagrams / वेन आरेख, Deduction, Induction and Analogy / निगमन, आगमन एवं सादृश्यता, Fallacies / तर्कदोष, Indian Logic: Pramanas / भारतीय तर्कशास्त्र: प्रमाण, Anumana and Vyapti / अनुमान एवं व्याप्ति, Hetvabhasa / हेत्वाभास, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Aristotle / अरस्तू, Western Schools of Philosophy / पाश्चात्य दर्शन की विचारधाराएँ, Kant / कांट, Sadhana Paada, Vaiśeṣika / वैशेषिक
  7. Paper - 1 | Unit - 7 | Data Interpretation: Data and Graphical Representation / आँकड़े एवं आलेखीय निरूपण, Data Interpretation: Tables / आँकड़ा निर्वचन: तालिका
  8. Paper - 1 | Unit - 8 | Information and Communication Technology: Computer Fundamentals and Hardware, Memory, Storage and Data Representation, Computer Software, Office Applications, Multimedia and File Formats, Computer Networks, Internet and World Wide Web, Email and Online Communication, Cyber Security, Digital Ethics, IPR and Society, Cloud and Distributed Computing, Emerging Technologies, ICT in Education and Governance, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Electronic Data Interchange and E-Commerce, Internet Fundamentals, Web Design & Development, Web Publishing & Hosting, Emerging Technologies, Terms & Abbreviations, Society, Law & Ethics, Keyboard Shortcuts, Website, Browser & Services, Protection of Geographical Indications / भौगोलिक संकेतों का संरक्षण
  9. Paper - 1 | Unit - 9 | People Development and Environment: Ecosystems and Biodiversity / पारितंत्र और जैव विविधता, Human and Environment Interaction / मानव और पर्यावरण की अंतःक्रिया, Development and Environment / विकास और पर्यावरण, Natural Resources – Forests, Water and Soil / प्राकृतिक संसाधन: वन, जल और मृदा, Energy Resources / ऊर्जा संसाधन, Air Pollution / वायु प्रदूषण, Water Pollution and Treatment / जल प्रदूषण और उपचार, Noise Pollution / ध्वनि प्रदूषण, Waste Management / अपशिष्ट प्रबंधन, Environmental Health and Toxicology / पर्यावरणीय स्वास्थ्य और विषविज्ञान, Climate Change and Global Environmental Issues / जलवायु परिवर्तन और वैश्विक पर्यावरणीय समस्याएँ, Natural Hazards and Disaster Management / प्राकृतिक प्रकोप और आपदा प्रबंधन, Indian Environmental Laws and Policies / भारतीय पर्यावरण कानून और नीतियाँ, International Environmental Agreements / अंतर्राष्ट्रीय पर्यावरण समझौते, Environment / पर्यावरण, Geography / भूगोल, Factory and Industry Systems / कारखाना और उद्योग व्यवस्थाएँ, Earth Materials, Surface Features and Processes, Communicable Diseases and Immunization / संक्रामक रोग और प्रतिरक्षण
  10. Paper - 1 | Unit - 10 | Higher Education System: Education in Ancient India / प्राचीन भारत में शिक्षा, Ancient Centres of Higher Learning / प्राचीन भारत के उच्च शिक्षा केंद्र, Colonial Education Policies and Commissions / औपनिवेशिक काल की शिक्षा नीतियाँ और आयोग, Colonial Colleges, Universities and Reformers / औपनिवेशिक कॉलेज, विश्वविद्यालय व सुधारक, Education Commissions and Policies after Independence / स्वतंत्र भारत में शिक्षा आयोग और नीतियाँ, National Education Policy 2020 / राष्ट्रीय शिक्षा नीति 2020, Types of Higher Education Institutions / उच्च शिक्षा संस्थानों के प्रकार, Learning Programmes and Academic Credits / अधिगम कार्यक्रम और अकादमिक क्रेडिट, Professional, Technical and Skill-Based Education / व्यावसायिक, तकनीकी और कौशल आधारित शिक्षा, Value Education and Environmental Education / मूल्य शिक्षा और पर्यावरण शिक्षा, Governance, Administration and Financing / शासन, प्रशासन और वित्तपोषण, Regulation, Accreditation and Ranking / उच्च शिक्षा का नियमन, प्रत्यायन और रैंकिंग
  11. Paper 2 | Unit 1 | Discrete Structures and Optimization: Propositional and Predicate Logic, Set Theory, Relations, Functions, Permutation, Combination and Probability / क्रमचय, संचय एवं प्रायिकता, Graph Theory, Group Theory, Digital Systems & Boolean Basics, Boolean Expression, Boolean Minimization, Optimization, Markov Chains
  12. Paper 2 | Unit 2 | Computer System Architecture: Logic Gates & Hardware, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Basics of COA, Register Transfer and Microoperations, Programming the Basic Computer, Instr Formats & Modes, Control Unit Design, Pipelining, Input Output Organisation, Cache Memory Organization, Multiprocessors
  13. Paper 2 | Unit 3 | Programming Languages and Computer Graphics: Language Design, C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, HTML Basics, XML, JavaScript-Basics, Java, Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing, OOPS with C++, Java Fundamentals, Array, String, IO & References, OOPS with Java
  14. Paper 2 | Unit 4 | Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Data Warehousing & Mining, Big Data Systems, NoSQL
  15. Paper 2 | Unit 5 | System Software and Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
  16. Paper 2 | Unit 6 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  17. Paper 2 | Unit 7 | Data Structures and Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  18. Paper 2 | Unit 8 | Theory of Computation and Compilers: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  19. Paper 2 | Unit 9 | Data Communication and Computer Networks: 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, Cloud Computing, Mobile Computing
  20. Paper 2 | Unit 10 | Artificial Intelligence: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Planning, Multi Agent Systems, Fuzzy Sets, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms
  21. Full Notes: Paper 1 Full Notes
  22. Paper 1 | Full Mock Tests:
  23. Paper 2 | Full Mock Tests:
  24. Paper 1 | Previous Year Papers:
  25. Paper 2 | Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive quick revision and practice session on Permutation and Combination, fundamental topics in combinatorics. The instructor begins by establishing the core definitions: Permutation is defined as selection plus arrangement, whereas Combination is strictly about selection. The lesson progresses through the mathematical formulas for nPr and nCr, explaining factorial notation (n!) as a prerequisite. A significant portion of the video is dedicated to solving diverse practice problems that apply these concepts in various contexts. These include arranging books by subject, handling identical items like colored balls or repeated letters in words (e.g., 'FUZZTONE', 'MARKER'), forming numbers within specific ranges, and calculating travel routes using the multiplication principle. The instructor emphasizes critical distinctions such as when to use permutations versus combinations, particularly in scenarios involving directionality (train tickets) or identical items. The session concludes with complex combination problems involving repeated alphabets and case-based enumeration, reinforcing the systematic approach required to solve non-standard combinatorial questions.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the topic of 'Basic Concepts' focusing on Permutation and Combination. He begins by writing 'Permutation' and defining it as arrangement, specifically noting the formula involving selection plus arrangement. He then writes 'Combination' below it and starts drawing a symbol, likely to contrast the two concepts. The board displays 'BASIC CONCEPTS' with 'Permutation -> arrange X (Selection + arrangement)' and 'Combination'. The instructor underlines key terms like 'arrange' to emphasize the distinction between the two mathematical operations.

  2. 2:00 – 5:00 02:00-05:00

    The instructor is distinguishing between permutation and combination on a whiteboard. He defines permutation as selection plus arrangement, underlining 'arrange' and crossing it out to emphasize the difference. He then begins writing that combination is solely about selection, drawing a visual analogy involving 'n balls' and selecting 'r balls'. The formulas for nPr and nCr are written out, along with a visual representation of selecting r balls from n balls. The concept of factorials is introduced with examples like 7!, 5!, and n! to explain the mathematical notation used in the formulas.

  3. 5:00 – 10:00 05:00-10:00

    The video segment spans from 365 to 500 seconds. The instructor is teaching permutation and combination concepts, specifically focusing on the formula for combinations (nCr). He demonstrates how to calculate 8C3 by expanding it into a fraction of products. The lesson then transitions to a practice problem involving arranging books of different subjects together, requiring the application of grouping concepts. The board shows '8C3 = 3 terms / 3 terms' and the question about Babita's bag containing books of History, Science, and Maths.

  4. 10:00 – 15:00 10:00-15:00

    The instructor is solving a permutation problem involving arranging books of different subjects together. He initially demonstrates the concept using individual book slots (B1, B2, etc.) and calculates 7! for total arrangements. He then transitions to a new method where books of the same subject are treated as single units or 'blocks' (Sci, Math) to solve for arrangements where subjects stay together. The visual focus moves between solving a word arrangement problem and illustrating the formula for permutations with repetition.

  5. 15:00 – 20:00 15:00-20:00

    The instructor transitions from a permutation problem involving arranging books by subject to a new question about arranging the letters in the word 'FUZZTONE' with vowels together. He then shifts to explaining a different permutation concept involving arranging 9 balls of different colors (4 red, 3 blue, 2 green) where items within the same color are identical. The visual focus moves between solving a word arrangement problem and illustrating the formula for permutations with repetition.

  6. 20:00 – 25:00 20:00-25:00

    The instructor transitions to a new permutation problem involving the word 'MARKER' with a specific constraint regarding vowels. He writes down the total number of arrangements as the sum of cases where vowels are together and not together, then begins to list specific conditions for arranging the letters. The problem asks for arrangements where three vowels are not together. The board displays options a. 500, b. 720, c. 240, d. 360.

  7. 25:00 – 30:00 25:00-30:00

    The instructor transitions from a permutation problem involving the word 'MARKER' to a new question about forming numbers between 500 and 1000 using specific digits without repetition. He initially writes 'with repetition' but then corrects the approach to solve for 'without repetition' as per the question text. The solution involves calculating permutations by considering the constraints on the hundreds, tens, and units places. He arrives at the final answer of 90 ways.

  8. 30:00 – 35:00 30:00-35:00

    The instructor is solving a permutation and combination problem involving forming groups of members. The question asks for the number of ways to form a group of 4 from 8 members under two conditions: including two particular members and excluding two particular members. The instructor demonstrates the calculation for the second condition, showing that selecting 2 members from the remaining 6 results in 15 ways. The board shows 'm1 m2 (m3) m4 m5 (m6) m7'.

  9. 35:00 – 40:00 35:00-40:00

    The instructor is solving a permutation and combination problem involving travel routes between three cities: Mirzapur, Delhi, and Jaunpur. He explains that to find the total number of ways to travel from Mirzapur to Jaunpur via Delhi, one must multiply the number of routes for each leg of the journey (8 routes from Mirzapur to Delhi and 6 routes from Delhi to Jaunpur). The calculation shown on the board is 8 multiplied by 6, resulting in 48 different ways.

  10. 40:00 – 45:00 40:00-45:00

    The instructor solves two distinct combinatorics problems involving permutations and combinations. First, he calculates the number of handshakes among 15 students using the combination formula 15C2, arriving at 105. Next, he addresses a railway ticket problem with 20 stops, initially calculating 20C2 as 190 but then correcting the logic to account for directionality (permutations), resulting in an answer of 380. The board shows 'CSK vs MI, MI vs CSK' to illustrate directionality.

  11. 45:00 – 50:00 45:00-50:00

    The instructor is solving a permutation and combination problem involving the alphabets A, B, A, B, B. He breaks down the solution by categorizing combinations based on the number of alphabets selected (0 to 5). He systematically lists the possible unique combinations for each category, such as 'AA', 'BB', 'AB' for two alphabets. The board shows options a) 10, b) 12, c) 11, d) None of these.

  12. 50:00 – 55:00 50:00-55:00

    The video segment covers a period from 3965 to 4250 seconds, likely focusing on a specific topic or event within this timeframe. The instructor is solving a permutation and combination problem involving the alphabets A, B, A, B, B. He breaks down the solution by categorizing combinations based on the number of alphabets selected (0 to 5). He systematically lists the possible unique combinations for each category, such as 'AA', 'BB', 'AB' for two alphabets.

  13. 55:00 – 60:00 55:00-60:00

    The video segment covers a period from 3965 to 4250 seconds, likely focusing on a specific topic or event within this timeframe. The instructor is solving a permutation and combination problem involving the alphabets A, B, A, B, B. He breaks down the solution by categorizing combinations based on the number of alphabets selected (0 to 5). He systematically lists the possible unique combinations for each category, such as 'AA', 'BB', 'AB' for two alphabets.

  14. 60:00 – 65:00 60:00-65:00

    The video segment covers a period from 3965 to 4250 seconds, likely focusing on a specific topic or event within this timeframe. The instructor is solving a permutation and combination problem involving the alphabets A, B, A, B, B. He breaks down the solution by categorizing combinations based on the number of alphabets selected (0 to 5). He systematically lists the possible unique combinations for each category, such as 'AA', 'BB', 'AB' for two alphabets.

  15. 65:00 – 70:00 65:00-70:00

    The video segment covers a period from 3965 to 4250 seconds, likely focusing on a specific topic or event within this timeframe. The instructor is solving a permutation and combination problem involving the alphabets A, B, A, B, B. He breaks down the solution by categorizing combinations based on the number of alphabets selected (0 to 5). He systematically lists the possible unique combinations for each category, such as 'AA', 'BB', 'AB' for two alphabets.

  16. 70:00 – 70:56 70:00-70:56

    The video segment covers a period from 3965 to 4250 seconds, likely focusing on a specific topic or event within this timeframe. The instructor is solving a permutation and combination problem involving the alphabets A, B, A, B, B. He breaks down the solution by categorizing combinations based on the number of alphabets selected (0 to 5). He systematically lists the possible unique combinations for each category, such as 'AA', 'BB', 'AB' for two alphabets.

The lecture systematically builds understanding of Permutation and Combination through definition, formula derivation, and extensive problem-solving. The instructor establishes that Permutation involves both selection and arrangement (nPr), while Combination is strictly about selection (nCr). This distinction is reinforced through visual aids like selecting balls from a set and writing out factorial expansions. The practice section covers a wide array of scenarios: arranging items with constraints (books by subject, vowels in words), handling identical items (colored balls, repeated letters), and applying the multiplication principle to travel routes. A key pedagogical moment occurs when distinguishing between combinations (handshakes) and permutations (train tickets), highlighting the importance of directionality. The final problems involve complex enumeration with repeated alphabets, requiring case-by-case analysis to count unique combinations. The instructor consistently uses board work to visualize constraints and calculations, ensuring students can follow the logical steps from problem statement to solution.

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