Learn more about permutations and how to evaluate them using these techniques. A useful lesson for math students of class 11/12. A good foundation of permutations is useful in competitive exams.
Learn what are circular permutations and how to evaluate them. Also learn how to evaluate permutations when clockwise and anticlockwise arrangements are indistinguishable.
WHAT ARE COMBINATIONS?
Learn about combinations and what distinguishes it from Permutations. Relevant formulas are illustrated through problems. A useful tool for mathematics students of Classes 11 and 12.
MIXED PROBLEMS ON PERMUTATIONS AND COMBINATIONS
Learn mixed problems in permutations and combinations. This is greatly useful for Class 11 and 12 Math, NCERT and ISC. You will learn how to combine permutations and combinations in solving problems. This lesson is the most crucial part on this course on Permutations and Combinations.
BINOMIAL THEOREM-AN INTRODUCTION
What is the Binomial Theorem? The Binomial Theorem shows you how to find the powers of binomial expressions like a+b,
a-b. Learn the basic formulas of Binomial Theorem and a few simple problems.
Watch this video to learn how to expand using Binomial Theorem. A number of useful formulas are mentioned in this video. Lean how to find the number of terms of a Binomial expansion.
GENERAL TERM OF A BINOMIAL EXPANSION
Learn how to find the general term of a Binomial expansion. Notice how you can use this formula to find any term of an expansion.
MIDDLE TERM OF A BINOMIAL EXPANSION
You will learn how to calculate the middle term/terms of a Binomial expansion. Note that, when n is even, there are n+1 terms, hence one middle term. If n is odd, there are even number of terms. Hence there are 2 middle terms. You can view the formula and a solved problem by clicking on this link.
HOW TO FIND THE TERM INDEPENDENT OF X
2 types of problems are discussed here. Firstly, we learn to find the term independent of x, using the formula for the r th term of a binomial expansion. Then you learn how to find the r th term from the end in any binomial expansion. You will understand that it is as simple as finding the r th term from the beginning, that is, the rth term.