The counting question: how many lattice paths are there between \((0,0)\) and \((3,2)\text{?}\) We could try to draw all of these, or instead of drawing them, maybe just list which direction we travel on each of the 5 steps. One path might be RRUUR, or maybe UURRR, or perhaps RURRU (those correspond to the three paths drawn above). So how many such strings of R's and U's are there?
in-context