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Explore fundamental counting techniques in discrete mathematics through this 78-minute lecture from MIT's Principles of Discrete Applied Mathematics course. Learn about binomial coefficients and bijections while mastering the powerful technique of counting objects in multiple ways to establish mathematical relationships. Discover how Catalan numbers emerge as a unifying concept that counts seemingly different combinatorial structures including Dyck paths, plane trees, and binary trees, demonstrating the elegant connections between various mathematical objects through bijective proofs.
