What if my movie marathon consists of exactly five distinct movies: two movies from one of the trilogies, 2 movies from a 2nd trilogy, and 1 movie from a 3rd. The movies can be watched in whatever order I choose and the same five movies watched in a different order constitute a different marathon. Now how many movie marathons are possible?

A medical Centre can have many doctors. A doctor can be scheduled for many appointments but may not have any scheduled appointment at all. A patient can schedule request for one or more appointments. However, every appointment is about only one patient. As a result of every appointment, there must be a bill. One payment is applied to exactly 1 bill, and 1 bill can be paid off over time by several payments. A bill can be outstanding, having nothing yet paid on it at all. One patient can make many payments, but a single payment is made by only 1 patient. Some patients are insured by an insurance company. If they are insured, they can only carry insurance with one company. An insurance company can have many patients carry their policies. For patients that carry insurance, the insurance company will make payments, each single payment is made by exactly 1 insurance company. (Hint: final ERD must include 7 tables.) a) Identify the entities with attributes and keys (primary and foreign keys).…

There are m towns in a straight line, with a road joining each pair of consecutive towns. Legends say that an ordinary person in one of these towns will become a hero by completing a sequence of n quests. The first quest will be completed in their home town, but after each quest they may complete their next quest either in the same town or after moving to a neighbouring town.For example, if n = 5 and m = 4, a resident of town 2 may become a hero as follows:• begin in town 2 for quest 1,• then move to town 3 for quest 2,• stay in town 3 for quest 3,• return to town 2 for quest 4, and• move to town 1 for quest 5.Design an algorithm which runs in O(nm) time and finds the total number of waysto complete n quests.

imagine that as example We have a  transportation company operates individual taxis and shuttles. It uses its taxis for transporting in the form of an individual or small group from one location to another. On the other hand, the shuttles have different scenario.  They are used to pick up individuals from separate locations and provide them conveyance to several destinations. Any individual can call the company from anywhere. It may be a hotel, a mall, entertainment venue or any tourist company. When the company receives a call from such individuals, it tries schedule any available taxi for pickup service for fee-based If There's no available taxi,  it does not operate any form of queuing system. Means " If there is no available car, the order is lost " If the vehicles are available, the individual confirms for pick-up. After arrival at the pick-up place the driver notify the company that it has picked up the passenger. The driver notifies the company again at the time of dropping him…

My colleague, Dr. Strange tells me that there is an alternate universe where Sydney buses are never cancelled and they always run on time; in fact, bus timetables specify to the second the exact arrival and departure time of each bus on each stop. Sadly, in this alternate reality there are no free transfers (i.e., you need to pay for the full fare of every bus you ride) and different bus lines charge different fees (but the good news is that the fee is flat and does not depend on distance travelled). A travel plan is a sequence of stop-time pairs where stop is a location of a bus stop and time is when we arrive at that stop. The plan is feasible if for any two consecutive pairs (a, t) and (b, t′) in the plan there exists a bus that departs after t and arrives at b at exactly t′. That is, a travel plan does not allow us to walk between stops. Assuming that no two buses arrive at the same time at the same stop, a feasible plan uniquely identifies the bus lines that we need to take to…

In how many ways can 3 different novels, 4 different mathematics books, and 1 biology book be arranged on a bookshelf if (1) the books can be arranged in any order? (2) the mathematics books must be together but the other books can be arranged in any order? (3) the mathematics books must be together and the novels must be together?