Marinada '23

[lang=hr] Odredite $n$ u sljedećim dvjema jednadžbama (nisu povezane). Rješenje zapišite u obliku $x,y$ gdje je $x$ rješenje gornje, a $y$ donje jednadžbe. $$\binom{n}{n-2}=\binom{n}{n-5}$$ $$\binom{n^2}{10}=\binom{n^2}{15}$$ \\ \textit{Napomena:} Za prirodne brojeve $n,k$ vrijedi $\binom{n}{k}=\frac{n!}{k!(n-k)!}$. [/lang] [lang=en] Solve the following two equations for $n$ (the equations are not connected). Write your solution in the form $x,y$ where $x$ is the solution of the first equation, and $y$ the solution of the second equation. $$\binom{n}{n-2}=\binom{n}{n-5}$$ $$\binom{n^2}{10}=\binom{n^2}{15}$$ \\ \textit{Note:} For nonnegative integers $n,k$ is $\binom{n}{k}=\frac{n!}{k!(n-k)!}$. [/lang]