69 lines
1.9 KiB
TeX
69 lines
1.9 KiB
TeX
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\documentclass[12pt,a4paper,german]{article}
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\usepackage{url}
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%\usepackage{graphics}
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\usepackage{times}
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\usepackage[T1]{fontenc}
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\usepackage{ngerman}
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\usepackage{float}
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\usepackage{diagbox}
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\usepackage[latin1]{inputenc}
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\usepackage{geometry}
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\usepackage{amsfonts}
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\usepackage{amsmath}
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\usepackage{csquotes}
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\usepackage{graphicx}
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\usepackage{epsfig}
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\usepackage{paralist}
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\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}
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%%%%%%%%%% Fill out the the definitions %%%%%%%%%
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\def \name {Valentin Brandl} %
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\def \matrikel {108018274494} %
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\def \pname {Marvin Herrmann} %
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\def \pmatrikel {108018265436} %
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\def \gruppe {Mi 10-12 (Andre)}
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\def \uebung {1} %
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% DO NOT MODIFY THIS HEADER
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\newcommand{\hwsol}{
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\vspace*{-2cm}
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\noindent \matrikel \quad \name \hfill \"Ubungsgruppe: \gruppe \\
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\noindent \pmatrikel \quad \pname \\
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\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center}
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}
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\begin{document}
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%Import header
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\hwsol
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\section*{Aufgabe 1.2}
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\begin{enumerate}[(1)]
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\item
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\begin{eqnarray*}
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\binom{16}{8} \cdot \binom{8}{2} \cdot \binom{6}{2} \cdot \binom{4}{2} \cdot 2! &=& 64864800
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\end{eqnarray*}
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\item
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\begin{itemize}
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\item Figuren werden farblich unterschieden
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\begin{eqnarray*}
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\binom{64}{8} \cdot \binom{56}{8} \cdot \binom{42}{2} \cdot \binom{40}{2} \cdot \binom{38}{2} \cdot
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\binom{36}{2} \cdot \binom{34}{2} \cdot \binom{32}{2} \cdot 30 \cdot 29 \cdot 28 \cdot 27 = \\
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= 342252222360871944253577108738801126400000 \\
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= 3.4 \cdot 10^{41}
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\end{eqnarray*}
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\item Figuren werden farblich nicht unterschieden
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\begin{eqnarray*}
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\binom{64}{16} \cdot \binom{42}{4} \cdot \binom{38}{4} \cdot \binom{34}{4} \cdot \binom{30}{2} \cdot
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\binom{28}{2} &=&
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30778963276000023764494761426480000 \\
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&=& 3.1 \cdot 10^{34}
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\end{eqnarray*}
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\end{itemize}
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\end{enumerate}
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\end{document}
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