[tex]\dfrac{18!}{y!(18-y)!}=\dfrac{18!}{(y+2)!(16-y)!} \\ \\ \\y!(18-y)! = (y+2)!(16-y)! \\ \\y!(16-y)!(17-y)(18-y) = y!(y+1)(y+2)(16-y)! \Big|:y!(16-y)! \\ \\ (17-y)(18-y)=(y+1)(y+2)\\ \\\Rightarrow 17-y = y+1 \Rightarrow 2y = 16 \Rightarrow y = 8\quad \text{(se observa ca verifica.)}\\ \\\\ \Rightarrow S = \big\{8\big\}[/tex]
