Production line workers assemble 15 automobiles per hour. During a given hour. four are produced with improperly fitted doors. Three automobiles are selected at random and inspected. Let X denote the number inspected that have improperly fitted doors.
(a) Find the density for X.
(b) Find E[X] and Var X.
(c) Find the probability that at most one will be found with improperly fitted doors.