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Counting Principles and Counting Formulas; Pigeonhole Principles and Mean Value Principles; Generating Functions; Recurrence Sequence of Numbers; Classification and Method of Fractional Steps; Corresponding Method; Counting in Two Ways; Recurrence Method; Coloring Method and Evaluation Method; Proof by Contradiction and Extreme Principle; Locally Adjusted Method; Constructive Method; Combinatorial Counting Problems; Existence Problems and the Proof of Inequalities in Combinatorial Problems; Combinatorial Extremum Problems.