10. An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 20% of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate.

(a) Let X be the number of passengers that show up out of 6 reservations. What is the distribution of X and why?

(b) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip?

(c) If six reservations are made, what is the expected number of available places when the limousine departs?