(i) Automobile license plates in California usually consist of one digit, followed by three letters, followed by three digits (for example, 4EVA530). The first digit is never zero. How many different plates of this type could be made? (ii) Look up the population of California. Assuming that every resident of California has at least one (registered) car, could the DMV use the three letter + three number system from Exercise F to make license plates for all of California? The president of the Mathematics and Computer Club would like to arrange a meeting with ten attendees, the president included. There will be five computer science majors and five math majors at the meeting. How many ways can the ten people be seated at a circular table if the president does not want people with the same major to sit next to one other? (Note: we don't care about the location of the seats in the room, only the circular ordering of the seating arrangement.)