2. [16 points] Four clients requested appointments at a service station in a given week. Each appointment is on one of the five working days (some appointments may be arranged during the same day). Answer the following questions. (a) [1 point] How many ways can one assign each of the four appointments to a day of the week. (b) [4 points] How many arrangements from (a) are such that no day has more than one appointment? More than two appointments? (c) [5 points] How many arrangements from (a) are such that there is an appointment on Monday? There are appointments on both Monday and Tuesday? (d) [3 points] How many arrangements from (a) have exactly three days taken for appointments? (e) [1 point] Let (x1, 2, z3,x4,x5) denote the workload profile, where x; is the number of appointments on day 7. How many different workload profiles are there for four appointments? (f) [2 points] How many workload profiles from (e) are such that no day has more than two appointments