# Combinatorics

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## Fundamental Counting Principles

"How do I love thee? Let me count the ways!" As choices increase in number, counting techniques are fundamental in determining the number of possible outcomes and orders. Explore the principles that form the basis of combinatorics.

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## Binomial Coefficients

In situations where order is not important, binomial coefficients are used to calculate the number of possible combinations given a set number of choices. Begin practicing basic combinations and counting techniques.

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## The Pigeonhole Principle

A useful tool in combinatorics, the Pigeonhole Principle lets us assume that if $m$ items are placed in $n$ categories, and $m > n$, some categories must contain more than one item. Apply the consequences of this simple, but powerful, principle.

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## Distribution Problems

Utilize different techniques of distributing distinct or identical objects into boxes. Continue by exploring partitions and compositions of integers.

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## Inclusion-Exclusion

Take Venn Diagrams to the next level through examining the cardinality of the unions and intersections of sets.

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## Other Combinatorics Topics

Explore the various topics in combinatorics that don't fall 'discretely' into another theme: Latin Squares, Coding Theory, Ramsey Numbers, and more!

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