How many routes are there from the top-left to the bottom-right of a grid, moving only right or down? Each cell can be reached from the cell above or the cell to the left, so its count is the sum of those two. The top row and left column have exactly 1 route each:

def grid_paths(rows, cols):
    table = [[1] * cols for _ in range(rows)]
    for r in range(1, rows):
        for c in range(1, cols):
            table[r][c] = table[r - 1][c] + table[r][c - 1]
    for row in table:
        print(row)
    return table[rows - 1][cols - 1]

print(grid_paths(3, 4))

[[1] * cols for _ in range(rows)] builds a separate list for each row. (Writing [[1] * cols] * rows would make every row the same list, a classic bug.)