Marinada '25

[lang=hr] Dana je $2023 \times 2023$ ploča u kojoj su sva polja obojana ili crveno ili crno prema sljedećim pravilima: \begin{itemize} \item Svaki red ima različit broj crvenih polja \item Svaki stupac ima različit broj crnih polja. \end{itemize} Na koliko različitih načina možemo obojati ploču? Rješenje zapiši u obliku $a\cdot (b!)^c$ te kao odgovor na ovo pitanje napiši $a+b+c$ [/lang] [lang=en] Consider a $2023 \times 2023$ board whose cells are colored either red or black according to the following rules: \begin{itemize} \item Each row contains a distinct number of red cells. \item Each column contains a distinct number of black cells. \end{itemize} In how many different ways can the board be colored? Write the solution in the form $a\cdot (b!)^c$, and as the answer to this question give $a+b+c$. [/lang]