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This lecture covers topics in combinatorial mathematics, including permutations, combinations, binomial coefficients, and multinomial coefficients. The instructor explains the properties of binomial coefficients and demonstrates their applications in various scenarios. The lecture also delves into the concept of partitions of integers and the exponential series. Additionally, it introduces a small lexicon of mathematical terms related to probability and statistics, such as sample space, event space, and probability distribution. The presentation concludes with a discussion on probability spaces and the independence of events.