[tex]C_n^2=120\\\\
\dfrac{A_n^2}{P_2}=120\\\\
\dfrac{n(n-1)}{1\cdot 2}=120\\\\
n(n-1)=2\cdot 120\\\\
n^2-n=240\\\\
n^2-n-240=0\\\\
n_{12}=\dfrac{1\pm\sqrt{1+4\cdot 240}}{2}=\dfrac{1\pm\sqrt{961}}{2}= \dfrac{1\pm31}{2}\\\\
n_1=\dfrac{1+31}{2}=\dfrac{32}{2}=16\\\\
n_2=\dfrac{1-31}{2}=\dfrac{-30}{2}=-15~\notin N \\\\
\Longrightarrow~~\boxed{\bf n=16}[/tex]
