Door keys for a certain automobile are made from a blank key on which five cuts are made. Each cut may be one of five different depths.

(a) How many different keys can be made? 

(b) If 400,000 of these automobiles are made such that each of the keys determined in part (a) opens the same number of cars, determine how many cars can be opened by a specific key.

(c) If one of these cars is selected at random, what is the probability that the key selected at random will unlock the door?