Concept & Short Tricks of Derangement in P&C

Duration: 11 min

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Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Section 1 | भाषा (हिंदी) / Language (Hindi): भाषा, लिपि और वर्ण, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, पद-भेद और रूप-विकार, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, शब्द-भंडार, अपठित बोध, बहुविषयक सामग्री (विभिन्न अवधारणाओं से संबंधित सामग्री), वर्णमाला
  3. Section 1 | اردو زبان / Language (Urdu) — 22 Questions (Fixed): رسم الخط، حروفِ تہجی اور املا, اسم، ضمیر اور صفت, الفاظ، محاورے اور ضرب الامثال, تفہیمِ عبارت، انشا اور ترجمہ, تفہیم
  4. Section 1 | বাংলা ভাষা / Language (Bengali) — 22 Questions (Fixed): শব্দার্থ, বাগধারা ও ভাষাশুদ্ধি, বাক্য ও বাচ্য, শব্দগঠন ও শব্দভান্ডার, অনুবাদ, বোধপরীক্ষণ ও রচনা
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Verbs and Tenses, Pronoun, Verb, Adverb, Prepositions and Conjunctions, Parts of Speech, Determiner, Conjunction, Modals, Transformation of Sentences, Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Structure and Common Errors, Reading Comprehension, Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning / प्राथमिक गणित एवं तर्कशक्ति: Ratio and Proportion / अनुपात और समानुपात, Divisibility Rules / विभाज्यता के नियम, Mixture and Alligation / मिश्रण और एलिगेशन, Permutation and Combination / क्रमचय और संचय, Number System / संख्या पद्धति, HCF and LCM / महत्तम समापवर्तक और लघुत्तम समापवर्त्य, Sequences, Series and Combinatorics / अनुक्रम, श्रेणी और संयोजन, Time, Speed and Distance / समय, चाल और दूरी, Series / श्रेणी, Coding-Decoding / कूट लेखन एवं कूट वाचन, Non-Verbal Reasoning / अशाब्दिक तर्क, Percentage / प्रतिशत, Average / औसत, Profit, Loss and Discount / लाभ, हानि और बट्टा, Simple and Compound Interest / साधारण और चक्रवृद्धि ब्याज, Time and Work / समय और कार्य, Solid Mensuration / घन क्षेत्रमिति, Age Problems / आयु संबंधी प्रश्न, Arithmetic / अंकगणित, Simplification, Indices and Surds / सरलीकरण, घातांक और करणी, Algebra / बीजगणित, Probability / प्रायिकता, Trigonometry / त्रिकोणमिति, Syllogisms / न्यायवाक्य, Seating Arrangement and Puzzles / बैठक व्यवस्था एवं पहेलियाँ, Blood Relations / रक्त संबंध, Direction and Distance / दिशा एवं दूरी, Analytical Reasoning (Counting Figures Reasoning) / विश्लेषणात्मक तर्क (आकृति गणना तर्क), Mathematical Operations and Missing Numbers / गणितीय संक्रियाएँ एवं लुप्त संख्या, Calendar and Clock / कैलेंडर एवं घड़ी, Clock / घड़ी, Cubes, Dice and Figure Counting / घन, पासा एवं आकृतियों की गिनती, Venn Diagrams, Syllogism and Inequalities / वेन आरेख, न्याय वाक्य एवं असमानता, Data Arrangement / आँकड़ों की व्यवस्था, Inequality / असमानता, Analogy and Classification / सादृश्यता एवं वर्गीकरण, Order and Ranking / क्रम एवं रैंकिंग, Sets, Relations, Functions and Discrete Mathematics / समुच्चय, संबंध, फलन और विविक्त गणित, Number Systems and Number Theory / संख्या पद्धति और संख्या सिद्धांत, Coordinate Geometry, Vectors and 3D Geometry / निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति, Polynomials, Equations and Complex Numbers / बहुपद, समीकरण और सम्मिश्र संख्याएँ
  7. Section 2 | General Awareness (GK + Current Affairs) / सामान्य जागरूकता (GK + समसामयिकी): Polity / राजव्यवस्था, Scientific Achievements and Research / वैज्ञानिक उपलब्धियाँ और अनुसंधान, Biology / जीव विज्ञान, State-Specific General Knowledge / राज्य विशेष सामान्य ज्ञान, Chemistry / रसायन विज्ञान, History / इतिहास, Geography / भूगोल, Indian Economy / भारतीय अर्थव्यवस्था, Environment / पर्यावरण, Current Affairs / समसामयिकी, Static General Knowledge / स्थैतिक सामान्य ज्ञान
  8. Section 3 | Computer System and Org. (CSO): Basics of COA, Floating Point Rep, Cache Memory Organization, Instr Formats & Modes, Programming the Basic Computer, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design
  9. Section 3 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control
  10. Section 3 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Process Synchronization
  11. Section 3 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  12. Section 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Shortest Path Algos
  13. Section 3 | Theory Of Computation & Compiler Design: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  14. Section 3 | Emerging Trends (AI, Societal Ethics & MS Office): Computer Fundamentals, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications, Trade, Marketing and Consumer Protection / व्यापार, विपणन एवं उपभोक्ता संरक्षण, Cyber Safety and Security, Computer Software, Operating System, Computer Networks, Word Processing (MS Word), Terms & Abbreviations, Presentation Software (MS PowerPoint), Internet of Things, Cloud Computing
  15. Section 3 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Maintenance and Configuration Management, Software Testing
  16. Section 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Section 3 | OOPS, C++, JAVA, HTML: OOPS with C++, Java, HTML Basics, CSS
  18. Section 3 | Java: Java Fundamentals, Array, String, IO & References, OOPS with Java
  19. Section 3 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  20. Section 3 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  21. Section 3 | Multimedia: Multimedia
  22. BPSC Previous Year Papers:
  23. BPSC Full Mock Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video is a lecture on combinatorics, specifically focusing on permutations, combinations, and derangements. The instructor begins by introducing the concepts of permutation and combination using a visual metaphor of a locked box, clarifying that permutation is order-sensitive while combination is not. The main topic is derangements, which are permutations where no element appears in its original position. The video presents a problem involving 5 gems and 5 boxes, where no gem can be placed in its corresponding box. The instructor explains the formula for derangements, denoted as d_n, which is d_n = n! * Σ((-1)^k / k!) for k from 0 to n. He demonstrates the calculation for d_4 and d_5, using a table of values for n, d_n, and n! to find the final answer. The lecture uses a digital whiteboard for writing equations and diagrams, and includes a brief, humorous meme to illustrate a point about the problem's complexity.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card that visually contrasts 'PERMUTATION' and 'COMBINATION' using a dice and a fruit basket. It then transitions to a slide titled 'Confused' which poses the question 'Should I unlock with Permutation or Combination?' and shows two locked boxes labeled 'Permutation' and 'Combination'. The instructor, Yash Jain, is visible in a small window, introducing the topic of permutations and combinations as part of a 'Basic To Advance' course. The slide also features a logo for 'Knowledge Gate Educator'.

  2. 2:00 – 5:00 02:00-05:00

    The instructor presents a problem on a digital whiteboard: 'There are 5 gems {g1,g2,g3,g4,g5} and 5 boxes {b1,b2,b3,b4,b5}. We are supposed to place exactly one gem in each box. Find number of ways to do so such that gem g(i) is not placed in box b(i) for all i={1,2,3,4,5}.' He explains that this is a classic problem of derangements, where no element is in its original position. He begins to write the formula for derangements, d_n = n! * Σ((-1)^k / k!) for k from 0 to n, and then starts to calculate d_4 as an example.

  3. 5:00 – 10:00 05:00-10:00

    The instructor continues the calculation for the derangement of 4 items, d_4. He writes out the formula: d_4 = 4! * [(-1)^0/0! + (-1)^1/1! + (-1)^2/2! + (-1)^3/3! + (-1)^4/4!]. He simplifies this to 24 * [1 - 1 + 1/2 - 1/6 + 1/24], which evaluates to 24 * [12/24 - 4/24 + 1/24] = 24 * [9/24] = 9. He then refers to a table of values for n, d_n, and n! to find that d_5 = 44. He concludes that the number of ways to place the 5 gems such that no gem is in its corresponding box is 44.

  4. 10:00 – 10:36 10:00-10:36

    The video concludes with a black screen displaying the text 'THANKS FOR WATCHING' in an orange and white box. The instructor's voice is heard saying 'Thank you for watching.' This is the final frame of the video, serving as an outro.

The video provides a clear and structured lesson on derangements, a key concept in combinatorics. It begins by establishing the foundational difference between permutations and combinations, using a relatable visual analogy. The core of the lecture is the application of the derangement formula to solve a specific problem. The instructor methodically breaks down the calculation, demonstrating the use of the formula for a smaller case (d_4) before applying it to the main problem (d_5). The use of a table of pre-calculated values for d_n and n! is a practical teaching aid. The overall progression is logical, moving from concept to formula to application, making the complex topic accessible to students.

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