Combinatorial Results

Combinatorial Results

Explore a comprehensive 6-hour tutorial on combinatorial results and probability theory. Delve into topics such as N choose k, n balls into k cells, Vandermonde's Identity, and the Birthday Problem. Learn how to calculate probabilities for various scenarios involving coins, dice, cards, and boxes. Discover practical applications through examples like poker hand probabilities, Farkle dice game, and the Kansas Keno lottery. Gain insights into discrete order statistics, hypergeometric distributions, and Catalan numbers. Use R software for exact probability calculations and simulations. Analyze real-world problems, including Lewis Carroll's Pillow Problem and the probability of reaching diagonal points in random walks.