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\begin{document}
{\sf KTH Matematik}
\begin{center} 
 {\bf 5B1118 Diskret Matematik \\
Kontrollskrivning 2 \\
M{\aa}ndagen den  22 Mars, 2004 \\}
\end{center}

\vspace{.3in}

\begin{itemize}
\item {\it Skrivtid:}{\bf 10:15-11:15.}
\item {\it Till{\aa}tna hj\"alpmedel: Minir\"aknare med sifferdisplay.}
\item {\it Motivering kr\"avs!}
\item {\it F\"or godk\"ant resultat kr\"avs minst 5 po\"ang.}
\end{itemize}

\vspace{.1in}

\noindent\framebox[15cm]{Personnummer:\hspace{12cm}}\\
\framebox[15cm]{Namn:\hspace{12cm}}\\

\vspace{.3in}

\begin{enumerate}
\item (3p) Best\"am talet $x$ om
$$\sum_{i=0}^{50}{50\choose i}8^i=x^{100}.$$

\vspace{.5in}

\item(3p) Hur m\aa nga arrangemang  av bokst\"averna i ordet ARRANGEMANG finns det? Hur m\aa nga av arrangemangen har inte tv{\aa} A brevid varandra ( till exempel, RR\underline{AA}NGEMANG \"ar ej godk\"ant)?
\vspace{.5in}

\item(3p) Best\"am antalet heltal l\"osningar till ekvationen:
$$x_1+x_2+x_3+x_4=32$$
med $x_i>0$ f\"or $i=1,2$, $x_3>2$ och $x_4\geq 3$.


\end{enumerate}

\vspace{1in}


betyg:
\begin{tabular}{|c|c|c|c|}\hline
Upp.(1)& Upp. (2)&Upp. (3)&Tot.\\ \hline
&&&\\ \hline
\end{tabular}
\newpage 
KTH, Matematik, 5B1118, KS2.\hspace{1in}Namn: 
\newpage 
KTH, Matematik, 5B1118, KS2.\hspace{1in}Namn: 
\newpage 
KTH, Matematik, 5B1118, KS2.\hspace{1in}Namn:
\end{document}