Consider a robot sitting at the $(0,0)$ in the plane. The only type of move it can make is to jump one unit to the right $($from $($x$,$ y$)$ to $($x $+1,$ y$))$ or jump one unit up $($from $($x$,$ y$)$ to $($x$,$ y $+1)).$ It needs to get to $(15,7).($a$)$ Describe a way to give the possible routes for the robot as strings in the alphabet $\{$R$,$ U$\}.($b$)$ Use this to count the number of possible routes for the robot