From 6f9a744599bd968b1e93b3ce26fa1839b78d4983 Mon Sep 17 00:00:00 2001 From: Elias Fierke Date: Fri, 24 Jul 2026 09:21:00 +0200 Subject: [PATCH] =?UTF-8?q?fix:=20anordnung=20binomialkoeffizienten=20war?= =?UTF-8?q?=20auch=20in=20der=20L=C3=B6sung=20falsch,=20aber=20lugga=20ist?= =?UTF-8?q?=20es=20beim=20=C3=9Cberarbeiten=20nicht=20aufgefallen?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- material/ab1_Lös.pdf | Bin 125765 -> 156540 bytes material/ab1_Lös.tex | 51 ++++++++++++++----------------------------- 2 files changed, 16 insertions(+), 35 deletions(-) diff --git a/material/ab1_Lös.pdf b/material/ab1_Lös.pdf index 71cd7da6576fcb5d332e45d64b5d088587d3b921..578dcd9ff4dad42f82c49b8b88d8d7a797ef598d 100644 GIT binary patch delta 143762 zcmb@tV{{-<)GZj>wrxAbUn^XuWx|uFh;By-d?T`5H1p9$%;Ty9z-o1I(F+Z z;F=r|e;$=UsvlT?`8R@6NyISK3jZMeS*F|J_aQoWICJIk=Z}9onPVipGe$58sq0Nw zm-ihO_R{rvI2gIP>&>jwB4h~|YT>rGYDb$l?~hK^l(`_sftKH8)w*O=jY}y3_rLa( 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\begin{definitionbox}[Binomialkoeffizient] - Der Binomialkoeffizient gibt die Anzahl der Möglichkeiten an, aus einer Menge mit $n$ Elementen $k$ verschiedene Elemente auszuwählen. - \end{definitionbox} - \end{minipage} - \hfill - % Zweites Bild - \begin{minipage}[t]{0.25\textwidth} - \centering - \[ - \binom{n}{k}=\frac{n!}{k!(n-k)!} - \] - \caption{Formel Binomialkoeffizienten} - \label{fig:bino} - \end{minipage} - \end{figure} - - - 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: @@ -354,34 +335,34 @@ \begin{circuitikz}[x=0.8cm,y=0.8cm] \draw (10.25,16.25) rectangle (13,14.875); - \node at (10.875,15.5625) {$\binom{0}{0}=1$}; + \node at (11.75,15.5625) {$\binom{0}{0}=1$}; \draw (8.875,14.875) rectangle (11.625,13.5); - \node at (9.5,14.1875) {$\binom{1}{0}=1$}; + \node at (10.25,14.1875) {$\binom{1}{0}=1$}; \draw (11.625,14.875) rectangle (14.375,13.5); - \node at (12.25,14.1875) {$\binom{1}{1}=1$}; + \node at (13,14.1875) {$\binom{1}{1}=1$}; \draw (10.25,13.5) rectangle (13,12.125); - \node at (10.875,12.8125) {$\binom{2}{0}=1$}; + \node at (11.75,12.8125) {$\binom{2}{1}=2$}; \draw (7.5,13.5) rectangle (10.25,12.125); - \node at (8.125,12.8125) {$\binom{2}{1}=2$}; + \node at (8.875,12.8125) {$\binom{2}{0}=1$}; \draw (13,13.5) rectangle (15.75,12.125); - \node at (13.625,12.8125) {$\binom{2}{2}=1$}; + \node at (14.375,12.8125) {$\binom{2}{2}=1$}; \draw (11.625,12.125) rectangle (14.375,10.75); - \node at (12.25,11.4375) {$\binom{3}{0}=1$}; + \node at (13,11.4375) {$\binom{3}{2}=3$}; \draw (8.875,12.125) rectangle (11.625,10.75); - \node at (9.5,11.4375) {$\binom{3}{1}=3$}; + \node at (10.25,11.4375) {$\binom{3}{1}=3$}; \draw (6.125,12.125) rectangle (8.875,10.75); - \node at (6.75,11.4375) {$\binom{3}{2}=3$}; + \node at (7.5,11.4375) {$\binom{3}{0}=1$}; \draw (14.375,12.125) rectangle (17.125,10.75); - \node at (15,11.4375) {$\binom{3}{3}=1$}; + \node at (15.75,11.4375) {$\binom{3}{3}=1$}; \end{circuitikz} \end{figure} \end{enumerate}