Combinatorics: Counting Methods

This lecture covers the basic principles of combinatorics, focusing on counting methods to determine the number of possible outcomes in different scenarios. Starting with the fundamental counting principle, the instructor explains how to calculate the total outcomes of multiple experiments. The lecture then delves into permutations, discussing ordered arrangements of items and the factorial notation. Examples are provided to illustrate the concepts, such as ranking rats based on abilities and forming committees from a group of people. The topic of combinations is also explored, introducing binomial coefficients to calculate the number of combinations when order does not matter.