[tex]\text{Numarul de submultimi cu doua elemente este:} \boxed{\binom{2}{n}}\\
\text{Prin urmare avem ca:}\\
\binom{2}{n}=10\\
\dfrac{n!}{2!\cdot (n-2)!}=10\\
\dfrac{(n-2)!\cdot(n-1)\cdot n}{2\codt (n-2)!}=10\\
\dfrac{(n-1)\cdot n}{2}=10\\
n^2-n=20\\
n^2-n-20=0\\
(n-5)(n+4)=0\Rightarrow n_1=5\\
~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow n_2=-4(\text{nu convine})\\
S:n=5
[/tex]
