Learn COMBINATORICS the Arts and Crafts of counting
4.5 (1 rating)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
411 students enrolled

Learn COMBINATORICS the Arts and Crafts of counting

COUNTING UNCOUNTABLE LOGICALLY
4.5 (1 rating)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
411 students enrolled
Created by Amit Tripathi
Last updated 2/2019
English
Current price: $11.99 Original price: $19.99 Discount: 40% off
3 days left at this price!
30-Day Money-Back Guarantee
This course includes
  • 2 hours on-demand video
  • 2 downloadable resources
  • 1 Practice Test
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
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What you'll learn
  • After completing this course you will be able to handle all counting problems that appears in tests like GRE, GMAT, DAT, ACT, IITJEE, JEE MAINS, MATHEMATICS OLYMPIADS, CAT etc.
  • Science of Counting uncountable
  • You will have a firm foundation of permutation, combinatorics, division into groups and derangement theory etc.
  • You will become more comfortable with permutations and combinations !
  • Solve Real World Problems Using Combinations and Permutations.
  • Know When to Use Combinations or Permutations.
  • You will have a firm foundation for pursuing more combinatorics.
  • This course will help you improve your grade by at least 10%.
  • Different cases of Permutations such as word formation, Circular Permutations, etc.
  • Application of Multinomial Theorem to solve problem of Permutations and Combinations
  • In this course you will learn Meaning of Factorial notation.
  • In this course you will learn Division into Groups.
  • In this course you will learn prime factorization and Exponent of Prime p in n!
  • In this course you will learn Derangement.
Requirements
  • You Just need to be familiar with basic mathematics i.e. addition, subtraction, multiplication and division and of course you must have eager to learn new ways of counting. Willingness to Learn and apply multiple approach will be an added advantage.
Description

About this Course

If you want to learn code and science behind counting, this course is for you. In  this course we will learn systematic and a logical way of counting to solve problems that require a huge counting. After this course you will be able to solve problems of type ' in how many ways this can be done " or "find the total number of ways of..."  . 

We’ll begin and build with the basic principles of counting, and as we proceed, we’ll develop some advanced techniques which can help us answer a lot of complex counting related problems and ultimately  count the uncountable!

We will also establish the fundamentals behind counting and develop smarter way of counting.

This course will cover


  • Fundamental Principle of Counting

  • Basic Counting Techniques.

  • Factorial

  • Arrangement of Objects.

  • Selection of Objects.

  • Permutations including Circular Permutations

  • Combinations

  • Application to Number Theory

  • Division into Groups

  • Arrangements in Groups

  • Arrangement of identical Objects.

  • Derangement

  • Multinational Theorem

  • Number of Rectangles and Squares

  • Exponent of Prime p in n!

  • And many many many problems.

Who this course is for:

  • Anyone with an interest in learning permutation and combinations

  • Anyone with preparing to take a standardized test like GRE, SAT, ACT

  • Anyone taking a college or high school course in combinatorics

Let us begin!

Happy intuitive learning !                                              

Who this course is for:
  • All Logical thinkers, GMAT, SAT, AP aspirants, students preparing for College entry tests, JEE Mains and IIT JEE Advanced. Math Beginner, Math Majors People interested in the math behind counting. computer science guys interested in mathematical logic. Anyone wanting to expand their mathematical knowledge. Coder and math lovers.
Course content
Expand all 14 lectures 01:49:56
+ Introduction
3 lectures 17:39

Fundamental Principle of Counting

If we want to do counting in a better way, we have to learn science behind counting. To do so we can categories counting into two fundamental principles.

Two fundamental principles of counting are the Addition Principle, Multiplication Principle.

All subsequent concepts, here will build upon these two principles.

To introduce the principles, we have taken an example of a car company and described fundamental theory of counting.


Preview 05:26
Problems on Fundamental Theory of Counting
06:20
Quiz on Fundamental theory of counting
5 questions
+ Permutation and combination
10 lectures 01:25:38

Practice Problems on fundamental theory of counting. Download it, attempt these problems and apply FTC. Solution is given for your reference. Don't see solution before attempting.

Arrangement of objects: Permutation formula
09:10
Selection of Objects: Combination
12:02

Permutation

We have seen in example of factorials that we need the same number of students as chairs to sit on. But what happens if there are not enough chairs?

I am taking an example, how many different possibilities are there for any 2 of 3 pupils to sit on 2 chairs?      

Note here that 1 pupil will be left standing, which we don’t have to include when listing the possibilities.

Let us start again by listing all possibilities:

To find a simple formula like the one above, we can think about it in a very similar way. There are 3 students who could sit on the first chair. Then there are 2 students who could sit on the second chair. We don’t care about the remaining 1 child left standing. Again we should think about generalizing this. We start like we would with factorials, but we stop before we reach 1. In fact we stop as soon as we reach the number students without chair. When placing 7 students on 3 chairs there are 7.6.5 ways.

Problems on Selection and arrangements
11:02

Practice test of Selection and arrangements of objects (previous two lectures)

Selection and arrangements of objects
5 questions
Arrangements of objects in a circular Table: Circular Permutation
08:24
Problems on Circular arrangements
06:07

Practice problems on Arrangement of objects in circular table

Arrangement of objects in circular table
5 questions
Division into groups
05:11
Problems on Division into groups
06:47
Miscellaneous Problems on Combinatorics
11:54

Basics of prime factorization theorem

Prime Factorization Theorem
07:33

Problems on Prime Factorization

Problems of Prime Factorization
07:28
+ Prime Factorization of Factorials
1 lecture 06:39

Prime Factorization of Factorials Numbers

Prime Factorization of Factorials
06:39