3. Scheduling appointments. 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) How many ways can one assign each of the four appointments to a day of the week. (b) How many arrangements from (a) are such that no day has more than one appointment? More than two appointments? (C) How many arrangements from (a) are such that there is an appointment on Monday? There are appointments on both Monday and Tuesday? (d) How many arrangements from (a) have exactly three days taken for appointments? (e) Let (21, 12, 13, 14, 15) denote the workload profile, where zi is the number of appointments 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. Scheduling appointments. 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) How many ways can one assign each of the four appointments to a day of the week. (b) How many arrangements from (a) are such that no day has more than one appointment? More than two appointments? (C) How many arrangements from (a) are such that there is an appointment on Monday? There are appointments on both Monday and Tuesday? (d) How many arrangements from (a) have exactly three days taken for appointments? (e) Let (21, 12, 13, 14, 15) denote the workload profile, where zi is the number of appointments 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