Problem 2: A bumpy way For a given n, we make a structure of bumps by placing 2n rows of bumps as shown in the figure below for n = 2 (2n 4 and thus 4 rows). When a ball is dropped as shown above, it moves either Left or Right upon hitting a bump. Let M be the set of paths that bring the ball on its way down to the exact middle of the last row, which is possible since the last row has 2n bumps (an even number) (c) (2 points) Find M (d) (2 points) How many paths don't bring the ball to the middle of the last row of bumps