9. Consider the grid shown below; one can imagine that it is a map of roads in a city. In this problem we consider the problem of moving from one corner of the grid to another. (a) Suppose that, starting at the point labeled A, you can go one step up or one step to the right at each move as long as you stay on the grid. If you end up at the point labeled B, how many different paths are there? (Hint: keep track ofpaths with a table like "up, right, right, sup-3'4 (b) Now suppose that we must go through the point labeled (1, and still can only go one step up or one step to the right at each move. How many paths are there?III (C) Now, suppose that we must instead avoid the point labeled C how many paths are there