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%%% file:      s2.tex                                                        %%%
%%% author:    Ján Komara                                                    %%%
%%% email:     komara@fmph.uniba.sk                                          %%%
%%% copyright: public domain                                                 %%%
%%% version:   2017/10/22                                                    %%%
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\begin{document}

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\title{2. domáca úloha z predmetu 1-AIN-121 Matematika (1) ZS 2017/18}

\author{Ján Komara}

%\date{}
\date{\today}

\maketitle

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\section*{1. príklad}

Spočítajte hodnotu nasledujúceho sumačného výrazu, 
t.j. vyjadrite jednoduchým vzorcom bez použitia sumy:
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\begin{align*}
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\sum_{n_1+n_2+n_3+n_4=10} \frac{(-2)^{n_1-n_3} 3^{n_2} }{n_1! n_2! n_3! n_4!}
.
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\end{align*}
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\subsection*{Riešenie 1. príkladu}

Táto časť obsahuje riešenie 1. príkladu.

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\section*{2. príklad}

Určite koeficient pri $x^7$ vo výraze $(3x^2 + 5x - 7)^6$.

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\subsection*{Riešenie 2. príkladu}

Táto časť obsahuje riešenie 2. príkladu.

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\section*{3. príklad}

Dvaja učitelia skúšajú súčasne skupinu 8 študentov, každý jeden predmet.
Každý študent odpovedá z jedného predmetu 30 minút.
Koľko existuje rozvrhov skúšania, ak požadujeme, 
aby skúšky skončili za štyri hodiny?

\emph{Pokyny.}
Výsledok vyjadrite pomocou súčtovej notácie $\Sigma$.

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\subsection*{Riešenie 3. príkladu}

Táto časť obsahuje riešenie 3. príkladu.

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\end{document}

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