1.1 An Introduction to Probability In basic mathematical terminology, probability of an event is described as the ratio of the favourable chances of that event to take place, and the total number of chances. This ratio, is a number between 0 and 1. In ideal cases, a probability of an event being 1 will refer… Continue reading
Week -13 | Combinatorics – 10
This is an optional module for those appearing only for the Engineering exams. Practice Problems Q-1) Find the number of 2 digit positive integers that are divisible by both of their digits. Q-2) How many ways are there to arrange the numbers 1,2,3…,64 on a 8×8 chessboard such that the numbers in each row and… Continue reading
Week -13 | Combinatorics – 9
In this module, we’d discuss a couple of counting strategies that maybe useful while solving problems related to the Olympiads. We’d illustrate these strategies with the help of examples. Ex-1) Let be integers greater than 1. Consider to be a set with elements, and let be subsets of . Assume that for any 2 elements , there… Continue reading
Week -13 | Combinatorics – 8
Practice Problems Q-1) There are p intermediate stations on a railway line between 2 points A and B. In how many ways can a train stop at 3 of the stations such that no 2 of the stopping stations are consecutive? Q-2) How many different numbers smaller than can be formed by the digits 0,1,2… Continue reading
Week – 12 | Combinatorics – 7
This is an optional module for students preparing for the engineering entrance exams. Q-1) Among 6 persons in a room, there are either 3 who know each other or 3 who are complete strangers Solution : Let us consider a hexagon with each person denoting a specific vertex of the hexagon. We join 2 vertices… Continue reading