Manufacturing and Product Development Suppose Target sells a combination lock, which is really a permutation lock, with 40 numbers, 0 to 39. The combination for each lock is set at the factory and consists of three numbers.
a. How many lock combinations are possible if numbers can be repeated?
b. If all lock combinations are equally likely, what is the probability of selecting a lock with only single-digit numbers in the combination?
c. Answer parts (a) and (b) if the lock combination must be three different numbers.