Solving Some Basic Questions on Permutation & Combination

Duration: 14 min

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Module outline

  1. About the Course: About the Course
  2. Section 1 | Language (Hindi): भाषा, लिपि, ध्वनि, वर्ण, अक्षर, स्वर, व्यंजन, मात्रा और संयुक्ताक्षर, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, 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, मुहावरे और लोकोक्तियाँ, अपठित गद्यांश और अपठित पद्यांश, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  3. Section 1 | Language (उर्दू भाषा — 22 प्रश्न (निश्चित)): Spelling & Diacritics, Grammar (اسم, فعل, صفت, ضمیر), Vocabulary, Idioms & Proverbs, Comprehension
  4. Section 1 | Language (বাংলা / बांग्ला भाषा — 22 प्रश्न (निश्चित)): Bangla Script and Sounds, Bangla Grammar and Usage, Bangla Word Formation and Vocabulary, Reading and Text Interpretation
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Verb, Adverb, Preposition, Articles, Determiner, Conjunction, Modals, Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Mensuration and Geometry, Age Problems, Arithmetic, Powers and Exponents (Surds and Indices), Algebra, Probability, Trigonometry, Syllogisms, Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence
  7. Section 2 | General Awareness (GK + Current Affairs): Polity, Physics, Biology, State Wise GK, Chemistry, History, Geography, Indian Economy, Environment, GK- Current Affairs, Static General Knowledge
  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): Artificial Intelligence, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications
  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
  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 permutations and combinations, presented by an instructor from Knowledge Gate Educator. The video begins with an introduction to the topic, using visual metaphors of a roulette wheel and a fruit basket to illustrate the difference between permutations (order matters) and combinations (order does not matter). The core of the lecture consists of several worked examples. The first problem asks for the number of ways to seat 10 people in 4 chairs, which is solved using the permutation formula P(n,r) = n! / (n-r)!, resulting in 10P4 = 10 × 9 × 8 × 7 = 5040. The second example calculates the total number of 5-lettered words from the 26 alphabets, first without repetition (26P5 = 26 × 25 × 24 × 23 × 22) and then with repetition allowed (26^5). The third problem involves finding the number of 3-digit numbers between 100 and 999 that do not contain the digit 7, which is solved by considering the available digits for each place value (8 choices for the hundreds, 9 for tens, and 9 for units, resulting in 8 × 9 × 9 = 648). The final example asks for the number of 5-lettered words that start with 'a' and end with 'z' without repetition, which is calculated as 24P3 = 24 × 23 × 22 = 12144. The video concludes with a 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card for a lesson on 'PERMUTATION & COMBINATION'. The title is split into two parts, with 'PERMUTATION' over a roulette table and dice, and 'COMBINATION' over a fruit basket and a pizza. This visual metaphor illustrates the core concept: permutations are about ordered arrangements (like a lock combination), while combinations are about unordered selections (like a fruit basket). The scene then transitions to a presentation slide titled 'Confused' with the question 'Should I unlock with Permutation or Combination?'. This slide features a cartoon detective with a magnifying glass, standing between two locked doors labeled 'Permutation' and 'Combination', visually representing the confusion students often feel. The instructor, Yash Jain Sir, is shown in a small window, and the video title 'APTITUDE PROBLEMS ON PERMUTATION & COMBINATION' is displayed on a large yellow background.

  2. 2:00 – 5:00 02:00-05:00

    The instructor presents the first problem: 'If we have 10 people and 4 chairs, what are the number of ways to seat them?'. The on-screen text clearly states the question. The instructor explains that this is a permutation problem because the order of seating matters. He writes the permutation formula P(n,r) = n! / (n-r)! and substitutes n=10 and r=4, writing 10P4. He then expands the formula as 10! / (10-4)! = 10! / 6!. He further simplifies this by writing out the factorial as 10 × 9 × 8 × 7 × 6! / 6!, and the 6! terms cancel out, leaving the final calculation of 10 × 9 × 8 × 7.

  3. 5:00 – 10:00 05:00-10:00

    The second problem is introduced: 'Find the total number of 5 lettered words??'. The instructor presents two sub-questions: a) No repetition allowed, and b) Repetition allowed. For part (a), he explains that there are 26 alphabets (A-Z) and 5 slots. He writes the calculation as 26 × 25 × 24 × 23 × 22, which is 26P5. For part (b), he explains that with repetition allowed, each of the 5 slots can be filled with any of the 26 letters, so the total is 26^5. The instructor then moves to the third problem: 'Number of numbers between 100-999 which does not contain 7?'. He explains that this is a 3-digit number problem. He identifies the available digits for each place: for the hundreds place, digits 1-9 are available, but 7 is excluded, so 8 choices (1,2,3,4,5,6,8,9). For the tens and units places, digits 0-9 are available, but 7 is excluded, so 9 choices each (0,1,2,3,4,5,6,8,9). He writes the calculation as 8 × 9 × 9.

  4. 10:00 – 13:54 10:00-13:54

    The final problem is presented: 'In how many ways can we form a 5 lettered word? No repetition, starting with 'a' and ending with 'z'.'. The instructor explains that the first and last positions are fixed. The first letter is 'a' and the last is 'z', so the middle three positions are the only ones that can vary. He states that there are 24 letters left to choose from (26 total minus 'a' and 'z'). He then calculates the number of ways to fill the 3 middle slots as 24P3, which is 24 × 23 × 22. He performs the multiplication to get the final answer of 12144. The video concludes with a black screen displaying the text 'THANKS FOR WATCHING' in an orange and white box.

The video provides a structured and practical introduction to permutations and combinations. It begins by establishing the fundamental difference between the two concepts using relatable visual analogies. The core of the lesson is a series of progressively challenging, real-world problems. The instructor methodically applies the permutation formula P(n,r) to problems involving seating arrangements and word formation, clearly demonstrating the step-by-step calculation. He also addresses the case of repetition allowed, which is a key variation. The final problem integrates multiple constraints (fixed start and end letters), reinforcing the application of the concepts. The overall teaching style is clear, with a focus on problem-solving methodology, making it a useful resource for students preparing for aptitude tests.

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