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
Category: Combinatorics
Week – 11 | Combinatorics – 4
1.1 Some Corner Cases We’ve almost covered the essence of combinatorics that are needed at a beginner’s level to start studying this beautiful topic. This will be the last editorial of this module for those of you who’d not like to pursue any advanced studies in this chapter. There’ll be another editorial on this topic… Continue reading
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 | Combinatorics – 1
1.1 Introduction Combinatorics, in a way, deals with the art of counting, and thus, a lot of problems in this regard will be dealing with counting the number of arrangements of a particular sequence. As trivial as it may sound, this branch of mathematics has been widely used in various fields like economics, physics and… Continue reading