Learn COMBINATORICS the Arts and Crafts of counting
- 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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- 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.
- 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.
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.
Arrangement of Objects.
Selection of Objects.
Permutations including Circular Permutations
Application to Number Theory
Division into Groups
Arrangements in Groups
Arrangement of identical Objects.
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 !
- 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.
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.
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.