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3. (10 pts) Answer the following questions about a scheduling system for assigning TAs to office hours. Within the system, every single TA and every single office hour time is assigned an integer ID. These IDs start with 1 and increment by 1. That is, if there is a TA with ID equal to 6, there must be TAs with IDs equal to 1, 2, 3, 4 and 5. The same restriction applies to the office hour IDs. Note that any office hour not assigned a TA will be covered by Professor Tannen. (a) Let p,g,r,s be integers with posr58. Consider the TAs with IDs ranging from p to r inclusive, and consider the office hour slots with IDs ranging from a to s, inclusive. How many distinct functions for assigning Tas to office hours are there? (The TAs are the domain and the office hours are the codomain) (b) Let n be a positive integer. Suppose there are n TAs and an office hour slots. How many distinct functions for assigning Tas to office hours are there, such that every TA is assigned an office hour with an ID that is either strictly less than their ID or greater than or equal to two times their ID? (ex. if n = 10, TA 4 can be assigned office hour, where