The Product Rule & The Sum Rule: AND Multiplies, OR Adds | Discrete Mathematics §6.1

Almost every counting problem is built from just two moves — and telling them apart comes down to a single word: "and" versus "or." In this video: the two foundations of counting, derived and worked on the board. The product rule — when a task is a sequence of choices done in order (AND), you multiply. The sum rule — when a task can be done one way OR another disjoint way, you add. We work assigning offices, counting length-7 bit strings, choosing a representative, and picking one project from several lists — then combine both rules in a single problem. New here? Start with the §6.1 section intro. This video is part of Discrete Mathematics · Counting (§6.1 — The Basics of Counting). Full section playlist → linked above / in the description on the channel. Made with the Engineering Simplified method: a calm, two-voice story lesson taught on a chalk-and-board, with every worked example written out step by step. Topic coverage follows Rosen, Discrete Mathematics and Its Applications (Chapter 6).