Explore fundamental combinatorics concepts in this 25-minute mathematics video that introduces basic counting problems through clear explanations and practical examples. Master the fundamental principle of enumeration, discover clever counting techniques, and learn the sieve theorem (inclusion/exclusion principle) for determining the number of elements in set unions. Progress through engaging segments covering initial counting challenges, block coloring applications, and a detailed three-part breakdown of the sieve theorem, culminating in a comprehensive formula derivation that solidifies understanding of these essential mathematical concepts.