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+\newcommand{\curtitle}{Pascalsches Dreieck} \title{\curtitle} \author{Fierke, Janik, Weidlich} @@ -213,7 +213,41 @@ \ifoot{\normalfont\normalsize Fierke, Janik, Weidlich} \section{\curtitle} + Im Stochastikunterricht ist dir sicherlich schoneinmal die Formel des Binomialkoeffienten begegnet: + \begin{definitionbox}[Binomialkoeffizient] + Der Binomialkoeffizient gibt die Anzahl der Möglichkeiten an, aus einer Menge mit $n$ Elementen $k$ verschiedene Elemente auszuwählen: + \[ + \binom{n}{k}=\frac{n!}{k!(n-k)!} + \] + \end{definitionbox} + Zum Warmwerden berechnen wir: + \begin{multicols}{3} + $\binom{3}{0}=$ \hrulefill\\\\ + $\binom{3}{3}=$ \hrulefill\\\\ + $\binom{7}{3}=$ \hrulefill\\\\ + + $\binom{5}{0}=$ \hrulefill\\\\ + $\binom{5}{5}=$ \hrulefill\\\\ + $\binom{4}{2}=$ \hrulefill\\\\ + + + $\binom{n}{0}=$ \hrulefill { }für $n\in\mathbb{N}$\\\\ + $\binom{n}{n}=$ \hrulefill { }für $n\in\mathbb{N}$\\\\ + + \end{multicols} + + \begin{enumerate} + \item Berechne nun nach folgender Regel: + \begin{center} + \textit{Die Summe des Steins ist die Summe der darüberliegenden Steine. } + \end{center} + \begin{figure}[H] + \centering + \includegraphics[width=0.7\linewidth]{pyramide_01} + \end{figure} + + \end{enumerate} \label{LastPage} \end{document}