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Combinatorics

Poker gives an opportunity to introduce combinatorial concepts ranging from the very basic to the very intricate. The reader is encouraged to explore with an example of using the general formula for enumerating multiset permutations. Working through the short example will build the confidence needed when enumerating the straight hands.

Enumerating all poker hands requires the ability to use binomial coefficients for either set or n-digit binary string enumeration. This ability is not fully developed but exposed. For those new to this enumeration technique, a real-world example of creating a work schedule with a simple constraint is given to help introduce this new way of thinking. The reader will also be exposed to the use of functions as a way to make clear mathematical thoughts.

  • Multiplication Principle
  • Multisets
  • Multiset Permuations
  • Binomial Coefficients
  • Poker Hand Enumeration