Respuesta :
EXPLANATION
We should think about it in terms of shortest paths on a lattice, such as the one on the left with example coordinates. The number of shortest paths to each lattice coordinate is seen in the grid on the right, but we'll get to that later.
Each rossing point of the grid lines has integer coordinates (x,y), where x represents the horizontal coordinate and y represents the vertical coordinate. Imagine traversing a path from the origin O(0,0) to any coordinate (x,y) that runs through the grid lines, following the shortest path to (x,y). These are the "shortest paths."
There may be several such paths leading to the same general point (x,y), but they all have x horizontal and y vertical measures. The target is to count the total number of shortest paths linking each (x,y) point on the lattice. The first method is to simply count the shortest paths between each lattice point. However, we don't go about it in a random manner; instead, we take the simple route and begin at the origin, working our way through and up the grid:
-There is 1 shortest path from (0,0) to (0,0) this is the path where we don't move.
-There is 1 shortest path from (0,0) to (1,0) and 1 shortest path to (0,1) in fact we can see that there will be only 1 path to each point on the x-axis and each point on the y-axis. So we will fill in those numbers on each lattice point along axes (like the right hand grid above).
