1.1 Principle of Inclusion and Exclusion This very important principle is a generalization of the Sum Rule to sets which need not be disjoint. Let’s say that we have 2 sets & . We look at the cardinality of the union of these 2 sets (We assume that students going through this module are familiar with… Continue reading
Tag: ISI
Week – 11 | Combinatorics – 3
1.1 Introduction to Generating Functions Consider a simple problem where we have to calculate the number of ways to choose 2 fruits from 5 distinct fruits. Let’s call them A,B,C,D,E. So we have 1 each of these 5 fruits and we need to choose 2 of them (ignoring the order). A simple way would be… Continue reading
Week -11 | Combinatorics – 2
1.1 Basic Cases and Circular Permutations In the last lecture we considered the basic concepts of permutations and combinations. Let’s consider a couple of examples further to ease the process of understanding these. Ex -1 Find the number of permutations of the word ‘TRIANGLE’. How many of these permutations start with ‘T’ and end with… Continue reading
Week – 10 | Inequalities – 4
Q-1) For the minimum value of is __ Q-2) If be the sides of a triangle, then the minimum value of is a) b) c) d) Q-3) For positive reals , is always a) b) c) d) Q-4) For positive reals in H.P which of the follwing… Continue reading
INMO – 1986 | A Problem on Polynomials
Q) If is a polynomial with integer coefficients and three distinct integers, then show that it is impossible to have Solution: The solution revolves around an important property of integer coefficient Polynomials, For any 2 integers , is always divisible by . So from this we have divides which implies divides , divides , divides . Once we have this, the remaining… Continue reading