0 points Consider an n n grid (indexed n-1). Say we want to draw a path from the lower left grid point (0,0) to the upper right grid point, (n -1,n 1) by travelling only east or north cell-by-cell (no back-tracking is allowed, so we cannot travel west or south). We are interested in how many different paths are there in terms of n. For example, for n = 4, the number of paths from (0,0) to (33) is 20 (see Figure 1). (a) At a particular grid point (i.j), how many ways are there of reaching this point in terms of adjacent grid points? b) How many paths are there from (0.0) to (n-1,n1 for n-5? Page 2 (0,3) 1 (1,3) 4 2,3) 10 3,3) 20 (0,2) 1 1,2) 3 (2,2) 6 3,2) 10 (0,0) 1 1,0 (2,0) 1 3,0) 1 Figure 1: Grid Example for n 4 (c) How many paths are there from (0,0) to (n-1,n-1) for n-10? d) Give a general formula in terms of n for the number of paths