Again assume that alice can not be the president and that ben can not be the treasurer. in problem 2 "we solved this using the g-t-b formula. here we will calculate the good (the ways without alice as president and without ben a treasurer) directly using the addition principle. we will partition the good ways into five disjoint groups (the groups come from the four ways that result from the fact that alice and ben both may or not be an officer, with the last way further divided so that the multiplication principle works). find the size of each of these five groups and add them together to find the number of goods ways (hint: it should match your answer from problem 2) (a) assume that neither alice or ben is an officer. 9.807 604 (b) assume that alice is an officer and ben is not an officer. zo 908 (c) assume that alice in not an officer and that ben is an officer. (d) assume that alice is the vice president and ben is an officer. (e) assume that alice is the treasurer and ben is an officer. find the total number of good ways.