From a547b7169b6db11d13a9b737c30fe1def55f994e Mon Sep 17 00:00:00 2001 From: Paul Duncan Date: Sat, 19 Nov 2022 17:06:00 -0500 Subject: add articles/combinations-and-permutations.md --- TODO.md | 1 + content/articles/combinations-and-permutations.md | 49 ++++++++++++++++++++++ .../combinations-and-permutations/definitions.svg | 1 + .../combinations-and-permutations/definitions.tex | 18 ++++++++ .../combinations-and-permutations/formulas.svg | 1 + .../combinations-and-permutations/formulas.tex | 18 ++++++++ 6 files changed, 88 insertions(+) create mode 100644 content/articles/combinations-and-permutations.md create mode 100644 static/files/articles/combinations-and-permutations/definitions.svg create mode 100644 static/files/articles/combinations-and-permutations/definitions.tex create mode 100644 static/files/articles/combinations-and-permutations/formulas.svg create mode 100644 static/files/articles/combinations-and-permutations/formulas.tex diff --git a/TODO.md b/TODO.md index 1eb6b92..3d7836a 100644 --- a/TODO.md +++ b/TODO.md @@ -385,3 +385,4 @@ this stuff may not make any sense. (led toggling, wifi) (looking at building outdoor sensor and submitting to weather.gov cwop, see ) +- combinations and permutations article (partial) diff --git a/content/articles/combinations-and-permutations.md b/content/articles/combinations-and-permutations.md new file mode 100644 index 0000000..eeba392 --- /dev/null +++ b/content/articles/combinations-and-permutations.md @@ -0,0 +1,49 @@ +--- +slug: "combinations-and-permutations" +title: "Combinations and Permutations" + +# date (optional for articles) +date: "2022-11-19T09:01:17-04:00" + +# show on articles page +show: true + +# uncomment to show table of contents +toc: false + +pics: + formulas: + css: "image" + tip: "Table of common combination and permutation formulas." + sources: + - src: "/files/articles/combinations-and-permutations/formulas.svg" + width: 1024 + height: 249 + + definitions: + css: "image" + tip: "Factorial and binomial coefficient definitions." + sources: + - src: "/files/articles/combinations-and-permutations/definitions.svg" + width: 1024 + height: 240 +--- + +Table of common combinations and permutations formulas. + +## Figures + +{{< pe-figure "formulas" >}} +{{< pe-figure "definitions" >}} + +## Source + +* [`formulas.tex`][formulas-tex]: [TeX][] source for `formulas.svg`. +* [`definitions.tex`][definitions-tex]: [TeX][] source for `definitions.svg`. + +[tex]: https://en.wikipedia.org/wiki/TeX + "Typesetting system commonly used for mathematics." +[formulas-tex]: /files/articles/combinations-and-permutations/formulas.tex + "Original TeX for formulas.svg." +[definitions-tex]: /files/articles/combinations-and-permutations/definitions.tex + "Original TeX for definitions.svg." diff --git a/static/files/articles/combinations-and-permutations/definitions.svg b/static/files/articles/combinations-and-permutations/definitions.svg new file mode 100644 index 0000000..279768f --- /dev/null +++ b/static/files/articles/combinations-and-permutations/definitions.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/static/files/articles/combinations-and-permutations/definitions.tex b/static/files/articles/combinations-and-permutations/definitions.tex new file mode 100644 index 0000000..6e81668 --- /dev/null +++ b/static/files/articles/combinations-and-permutations/definitions.tex @@ -0,0 +1,18 @@ +\begin{array}{|c|c|c|c|} +\hline + \text{Denoted} & + \text{Read As} & + \text{Formula} & + \text{Example} \\ +\hline + n! & + \text{"N factorial"} & + n! = \prod_{i=1}^n{i} & + 5! = 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 = 120 \\ +\hline + {n \choose k} & + \text{"N choose K"} & + {n \choose k} = \frac{n!}{k!(n - k)!} & + {5 \choose 3} = \frac{5!}{3!(5 - 3)!} = 10\\ +\hline +\end{array} diff --git a/static/files/articles/combinations-and-permutations/formulas.svg b/static/files/articles/combinations-and-permutations/formulas.svg new file mode 100644 index 0000000..06cb1b1 --- /dev/null +++ b/static/files/articles/combinations-and-permutations/formulas.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/static/files/articles/combinations-and-permutations/formulas.tex b/static/files/articles/combinations-and-permutations/formulas.tex new file mode 100644 index 0000000..b7a67ec --- /dev/null +++ b/static/files/articles/combinations-and-permutations/formulas.tex @@ -0,0 +1,18 @@ +\begin{array}{|l|c|c|c|} +\hline + \text{Name} & + \text{Ordered} & + \text{With Repetition} & + \text{Without Repetition} \\ +\hline + \text{Permutation} & + \text{Yes} & + n^k & + \frac{n!}{(n - k)!} \\ +\hline + \text{Combination} & + \text{No} & + {n + k - 1 \choose k} & + {n \choose k} \\ +\hline +\end{array} -- cgit v1.2.3