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%%% file:      s2.tex                                                        %%%
%%% author:    Ján Komara                                                    %%%
%%% email:     komara@fmph.uniba.sk                                          %%%
%%% copyright: public domain                                                 %%%
%%% version:   2019/10/27                                                    %%%
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\begin{document}

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\title{2. domáca úloha z predmetu 1-AIN-121 Matematika (1) ZS 2019/20}

\author{Ján Komara}

%\date{}
\date{\today}

\maketitle

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\section*{1. príklad}

Kompozíciou čísla $n$ rozumieme každú jeho usporiadanú partíciu v tvare
\begin{align*}
x_1 + \cdots + x_k = n
,
\end{align*}
kde $k \geq 1$ a $x_i \geq 1$ pre $i = 1,\ldots, k$.
Spočítajte počet kompozícií čísla $n \geq 1$.

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\subsection*{Riešenie 1. príkladu}

Táto časť obsahuje riešenie 1. príkladu.

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\section*{2. príklad}

Určite konštantný koeficient pri člene $x^5$ v úplnom rozvoji výrazu 
\[
\left(\frac{7}{x^2} + 8 - 9x\right)^{11}
.
\]

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\subsection*{Riešenie 2. príkladu}

Táto časť obsahuje riešenie 2. príkladu.

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\section*{3. príklad}

V 1. kole súťažilo proti sebe 10 dvojíc.
Koľkými spôsobmi môžeme z nich vytvoriť 10 nových súťažných dvojíc pre 2. kolo
(čiže žiadna dvojica s 1. kola sa nestretne opäť v 2. kole).

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

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\subsection*{Riešenie 3. príkladu}

Táto časť obsahuje riešenie 3. príkladu.

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\end{document}

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