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Combinatorics is often described briefly as being about counting, and indeed counting is a large part of combinatorics. As the name suggests, however, it is broader than this: it is about combining things. Questions that arise include counting problems: "How many ways can these elements be combined ?" But there are other questions, such as whether a certain combination is possible, or what combination is the "best" in some sense. We will see all of these, though counting plays a particularly large role.
Fundamentals.
Inclusion-Exclusion.
Generating Functions.
Systems of Distinct Representatives.
Graph Theory.
Polya–Redfield Counting.
Hints.
Index