Permutation & Combination One Shot | CA Foundation Quantitative Aptitude | Rahul Bhutani Sir 🔥

VishwasCA・2 minutes read

Understanding permutation and combination in numbers four to five is crucial for probability and theoretical studies, with various practical examples and calculations provided to solidify the concepts. The text delves into factorial methods, circular arrangements, and permutations with restrictions, emphasizing the importance of specific conditions and detailed calculations in different scenarios.

Insights

Understanding permutation and combination is crucial for probability and theory studies, emphasizing the importance of mastering foundational concepts.
The multiplication rule explains simultaneous tasks, while the addition rule is introduced for scenarios requiring one of multiple tasks to be done, showcasing different calculation methods.
Factorials play a key role in calculating permutations and combinations, with factorial values increasing with each number and simplifying complex calculations.
Arranging items with specific conditions, such as restrictions or preferences, involves applying formulas and selection processes to determine the number of ways items can be arranged, highlighting practical applications of permutation and combination theories.

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Recent questions

What is permutation and combination?
Permutation arranges, combination selects without order.
How is the multiplication rule applied?
Multiplication rule is used for simultaneous tasks.
What is the factorial method?
Factorial method calculates permutations and combinations.
How is the combination formula derived?
Combination formula simplifies to n! / (r! * (n-r)!).
How are items arranged with restrictions?
Items are arranged based on specific conditions.

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Summary

00:00

Mastering Permutation and Combination for Probability

The topic of today's class is permutation and combination, focusing on numbers four to five.
Understanding permutation and combination is crucial for further studies in probability and theory.
The importance of mastering this chapter is emphasized for a strong foundation.
Approximately 50 questions will be provided to showcase the variety of questions in exams.
The multiplication rule is explained for tasks that need to be done simultaneously.
Independent tasks can be done in n ways each, without any restrictions.
The addition rule is introduced for scenarios where one of multiple tasks needs to be done.
The total number of ways for independent tasks is calculated by adding the individual ways.
A practical example is given with selecting one boy and one girl from a class of 27 boys and 14 girls.
Another example involves creating a signal using two flags out of four different colors, resulting in four possible combinations.

12:29

Understanding Factorials and Color Combinations

To create two different colors, each color must be filled separately.
The pink color must be filled in the remaining three colors.
There are one, two, or three ways to fill the remaining colors.
Signals can be made in four ways when both colors are filled.
Five letters can be posted in four letter boxes in four ways.
The principle of counting will be clarified by understanding this concept.
Factorial is calculated by counting down from the number and stopping at one.
The value of factorials increases with each number, such as 8 factorial being 40320.
Factorials can be used to calculate permutations and combinations.
Factorials can be divided to simplify calculations, such as converting 6 factorial to 5 factorial.

24:39

Mathematical Operations and Factorials Explained

LCM took 61 in d1 plus 1 in 6 6 ba 6 e aqua me 7 6 ok it's done
My 7/6 = x ba 7 6 ok na 6 se 6
What is the value of multiply 49 one?
Brother, how much is the value of one?
X, has your 49 come?
The factorial of p 2 is my 12 in n fathole
Pay attention very carefully
Factorial is speaking to me pa
How to write this in factorial form
Permutation Determines the Number of Possible Arrangement Number of possible arrangements in a Set When the Order of the Arrangement Matters

37:37

Permutation Formula Simplifies Arrangement Calculations

Permutation formula involves filling three spaces with two numbers, one larger and one smaller, separated by a 'p'.
The factorial of the number above is divided by the factorial of the difference between the two numbers.
The answer to the arrangement is six, calculated as 3*2.
The formula states that arranging 'r' items out of 'n' spaces can be done in 'n' ways.
The factorial of the difference between the two numbers is crucial in the formula.
The factorial of negative numbers is not applicable in the formula.
The formula simplifies the arrangement of items in a given number of spaces.
Shortcut methods are introduced to quickly calculate permutations.
The formula is applied to various scenarios, such as finding the number of arrangements of letters in words.
Specific rules, like vowels being together, are incorporated into the formula for permutations.

51:11

Arranging Units and Letters: Formulas and Constraints

The text discusses arranging units and letters in different ways, focusing on vowels and units.
It explains the concept of arranging four units in four places, detailing the process and the formula involved.
The text delves into the internal arrangements of units, emphasizing the importance of keeping them together.
It further explores the arrangement of 10 examination papers, highlighting the need to avoid the best and worst papers coming together.
The text elaborates on the selection and arrangement of school prefects, considering the gender and position constraints.
It discusses the ways to arrange students, specifically five boys and three girls, for school prefect positions.
The text details the process of arranging the letters of the word "Triangles" to ensure the word "angle" remains intact.
It explains the circular arrangement concept, illustrating the positioning of individuals in a circular setting.
The text emphasizes the unique ways of seating individuals in a circular arrangement, focusing on the starting point and subsequent placements.
It concludes by highlighting the various positions and arrangements possible within a circular setting.

01:04:23

Circular Permutations: Factorial Method and Conditions

The text discusses circular arrangements and permutations, focusing on the factorial method.
It explains the process of arranging items in a circular manner, emphasizing the importance of the number of items.
The text delves into the concept of circular permutation, detailing the arrangement of individuals around a circular table.
It provides a step-by-step guide on arranging individuals in a circular manner, highlighting the factorial method.
The text explores scenarios where specific conditions are imposed on the arrangement, such as seating individuals based on height or gender.
It discusses the arrangement of individuals in a circular manner, ensuring that certain conditions are met, like not seating specific individuals together.
The text elaborates on the process of arranging a specific number of people in a circular manner while adhering to certain conditions.
It explains the concept of circular arrangements in the context of seating individuals around a table, considering various conditions and constraints.
The text provides detailed instructions on arranging individuals in a circular manner, focusing on the factorial method and specific conditions.
It concludes by discussing the arrangement of different items in a circular manner, emphasizing the factorial method and the importance of following specific conditions.

01:17:40

Arranging Items with Specific Conditions Formula

Permutation with restriction involves arranging items with specific conditions
Example given of distributing 5 glasses of Coca Cola to 10 girls, some of whom decline due to diet restrictions
Calculation of permutations with restrictions explained using the example of arranging 5 cold drinks
Formula for arranging items with specific conditions discussed, emphasizing the selection process
Application of the formula to arranging six different things taken three at a time, with one specific item always included
Detailed explanation of arranging items with restrictions, focusing on the selection process and remaining spaces
Formula for arranging items with restrictions further simplified for better understanding
Practical example provided of arranging different varieties of rice, bread, and sweets on a table with specific conditions
Internal arrangement of items with similar types discussed, emphasizing the grouping of similar items
Calculation of the number of three-digit numbers between 100 and 1000 without repetition, using the principle of counting and formulas for permutations

01:30:37

"Mathematical Formulas and Combinations Explained"

Two will be repeated multiple times at each position, while four will be repeated a specific number of times in every position.
Numbers have been assigned for each position, and if they are equalized, the unit place will be equal to the position.
When representing 100 p on tense, it is summed up to 120.
The formula involves multiplying one less number than the given digits by the factorial to get the sum of the digits and number of numbers.
Combination is explained using a selection process, where books are selected from a shelf based on Deera's preferences.
The combination formula is detailed as A P B I A factorial bi r factorial, which simplifies to n factorial by r factorial.
The process of selecting cards from a pack of 52 cards is explained, resulting in 2210 ways to select three cards.
Selecting three accountants from 10 applicants is calculated to have 120 possible ways.
The formula n + 1c n - 1 is used to determine the value of n, which is found to be 2 when the result is 45.
By reducing the total by one to two and taking the multiplication, the factorial of 2 is divided by 2 to achieve the result of 45.

01:44:46

"Number puzzles reveal mathematical relationships"

To find the value of n, multiply the given number by 45.
If you multiply the number by 90, it becomes one more than the original number.
Adding one to a number makes it one more than the original.
The number one less than the given number is smaller.
The bigger number is equal to or greater than the smaller number.
The value of 10 - 1 is 9.
To find the value of n+1 C n-1, the value becomes 45.
The simplified answer for n+1 * n divided by 2 is 45.
To find the value of r, divide 1680 by 70.
The factorial of 24 is the value of r.

01:58:04

"Arranging Men and Women in Specific Order"

The arrangement involves five men and four women sitting in a specific order, with women always occupying certain positions.
The second, third, and fourth positions are determined based on specific conditions.
If the sixth and eighth positions are even, then Vaman sits in four possible places.
The total number of arrangements for Vaman sitting in four places is calculated.
The number of true arrangements is determined using combinations.
Four steps are outlined to place four vomits in four different locations.
The process of vomiting is detailed, emphasizing the need to avoid repetition.
The arrangement of one doti cha pa at five places is discussed.
The ways to seat five people are calculated using permutations.
A formula is presented for permutations involving different types of items taken all at once.

02:10:06

"Mathematical Problem: Selecting Items for Picnic"

The number 2048 is significant, leading to the answer 47 in a mathematical problem.
The problem involves combinations of different types of items, with specific numbers of each type.
The scenario includes selecting items like donuts, waffles, and pastries for a picnic.
Various ways of selecting different quantities of items are explored, such as picking one, two, or more donuts.
Similar selection processes are applied to waffles and pastries, with different quantities and methods.
The total number of ways to select items for the picnic is calculated based on the different combinations.
The concept of arranging and selecting items based on their types and quantities is explained.
A scenario involving contributing different denominations of notes to a fund is presented.
The calculation of the number of ways to contribute to the fund is detailed.
The process of forming groups of items, such as letters in a word, is discussed, emphasizing selection over arrangement.

02:22:41

Majority rules in determining order of reverses.

The majority will determine the order of reverses, with options ranging from seven out of nine to nine out of eight or nine; the majority's decision will dictate the outcome, potentially leading to a reversal of the order based on the majority's choice.

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