3. Four Monash students will make medical appointments at Monash University Health Services in a given week. Each appointment is on one of five working days (some appointments may be arranged during the same day since there are many doctors). Answer the following questions. (a) How many ways can one assign each of the four appointments to a day of the week. [1] (b) How many arrangements from (a) are such that no day has more than one appointment? [4] How about more than two appointments? (c) How many arrangements from (a) are such that there is an appointment on Monday? [5] How about there are appointments on both Monday and Tuesday? (d) How many arrangements from (a) have exactly three days taken for appointments? [4] (e) Let (21, 12, 13, TA, 5) denote the workload profile, where r; is the number of appointments [1] on day i. How many different workload profiles are there for four appointments? (f) How many workload profiles from (e) are such that no day has more than two appointments? [3]