Solved Exercises in Counting Principles and Probability

This book offers a carefully curated collection of solved exercises in elementary and intermediate probability, with a primary focus on combinatorial techniques, foundational probability principles, and discrete structures. Designed for students in mathematics and related fields, the work emphasizes counting strategies, permutations, combinations, arrangements with or without repetition, and their application to classical probability problems. Core topics include the axioms of probability, conditional probability, independence, total probability, Bayes' theorem, and the analysis of finite sample spaces. The book does not rely on continuous or advanced probability distributions; instead, it builds a solid understanding of probabilistic reasoning through logical problem-solving, enumeration methods, and algebraic manipulation. Each chapter presents a progressive series of problems accompanied by detailed and pedagogically sound solutions aimed at fostering both conceptual clarity and technical proficiency. The structure is particularly suited for undergraduate coursework, competitive examination preparation, and guided self-study.