Hypergeometric Distribution
From charlesreid1
Hypergeometric distribution counts the number of ways you can obtain particular target values when sampling from a population without replacement.
This describes many systems - most notably a deck of 52 Cards (e.g. poker hands).
Hypergeometric distribution:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \displaystyle{ \dfrac{ \binom{K}{k} \binom{N-K}{n-k} }{ \binom{N}{n} } } }
where:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} K &=& \mbox{Successes} \\ N &=& \mbox{Pop. size} \\ k &=& \mbox{Targets} \\ n &=& \mbox{Sample size} \end{align} }
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Combinatorics
Combinatorial Structures - Order Does Not Matter Ordinary generating functions
Labelled Structures - Order Matters Enumerating Permutations: String Permutations Generating Permutations: Cool · Algorithm M (add-one) · Algorithm G (Gray binary code)
Combinatorics Problems Longest Increasing Subsequence · Maximum Value Contiguous Subsequence · Racing Gems Cards (poker hands with a deck of 52 playing cards)
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