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%%% author: Ján Komara %%%
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\title{2. domáca úloha z predmetu 1-AIN-121 Matematika (1) ZS 2021/22}
\author{Ján Komara}
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\date{\today}
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\section*{1. príklad}
Koľko celočíselných riešení má systém dvoch nerovníc
\begin{align}
x_1 + x_2 & < 4
\label{lt1}
\\
x_1 + x_2 + x_3 + x_4 + x_5 + x_6 & < 17
,
\label{lt2}
\end{align}
ak vyžadujeme, aby platilo
\[
-1 \leq x_1
\quad
2 \leq x_2
\quad
-3 \leq x_3
\quad
4 \leq x_4
\quad
-5 \leq x_5
\quad
6 \leq x_6
.
\]
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\subsection*{Riešenie 1. príkladu}
Táto časť obsahuje riešenie 1. príkladu.
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\section*{2. príklad}
Určite koeficient pri $x^6$ vo výraze $\left(5 - 4x^3 + \frac{3}{x^2}\right)^7$.
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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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