Q$.2$ Hotel St$.$ Jean has $240$ rooms. The hotel$$s housekeeping department is responsible for maintainingthe quality of the rooms$$ appearance and cleanliness. Each individual housekeeper is responsible for $20$rooms. Every room in use is thoroughly cleaned and its supplies, toiletries, and so on are restocked eachday. Any defects that the housekeeping staff notice that are not part of the normal housekeeping serviceare supposed to be reported to hotel maintenance. Every room is briefly inspected each day by ahousekeeping supervisor. However, hotel management also conducts inspection tours at random for adetailed, thorough inspection for quality$-$control purposes. The management inspectors not only checkfor normal housekeeping service defects like clean sheets, dust, room supplies, room literature, ortowels, but also for defects like an inoperative or missing TV remote, poor TV picture quality orreception, defective lamps, a malfunctioning clock, tears or stains in the bedcovers or curtains, or a