4 Question 4: Plan for Dining (28 pts) Lisa is a undergraduate student who is going to study in the library on a weekday and plans to have all of her 3 meals in the dining halls and restaurants around the library. There are 2 dining halls (named X and Y respectively) and 6 restaurants (named A, B, C, D, E, and F respectively, if needed) around the library for Lisa to choose among for her meals, and all of the 8 places above serve breakfast, lunch, and dinner. Also, suppose throughout this question that Lisa prefers to eat at DIFFERENT places for her different meals, which implies that she will end up with eating at 3 of the 8 places above on the weekday. (a) (5 pts) How many possible ways are there for Lisa to choose the places where she will have her meals on the weekday? Note: Here is an example effective throughout this question for your reference if relevant clarification is needed - a scheme in which Lisa has breakfast at A, lunch at X, and dinner at Y is different from one in which her has breakfast at A, lunch at Y, and dinner at X. (b) (7 pts) Suppose for THIS PART ONLY that Lisa will eat AT LEAST ONCE at (one or both of) the dining halls. How many possible ways are there for her to choose the places where she will have her meals on the weekday? Mike, a classmate of Lisa, will also have all of his 3 meals on campus on that weekday. Suppose throughout the rest of this question that, because Mike prefers to fully utilize his meal plan, he will only choose to eat at eith