A dealership has $n$ cars. An employee with a sense of humor takes all $n$ keys, puts one of them in each car at random, then locks the doors of all cars. When the owner of the dealership discovers the problem, he calls a locksmith. He tells him to break into a car, then use the key found in that car to open another, and so on. If and when the keys already recovered by this procedure cannot open any new cars, the locksmith is to break into another car. This algorithm goes on until all cars are open.
(a) What is the probability that the locksmith will only have to break into one car?
(b) What is the probability that the locksmith will have to break into two cars only?