A combination lock has four dials. On each dial are the digits 0 to 9.
a. Suppose you forget the correct combination to open the lock. How many combinations do you have to try? If it takes 10 s to enter each combination, how long will it take you to try every possibility?
b. Suppose you replace your lock with one that has five dials, each with the digits 0 to 9. How many combinations are possible? If it still takes 10 s to enter each combination, how long will it take to try every possibility?
c. For a lock to be secure, it has to be difficult for someone to guess the correct combination. How many times as secure as a 4-dial lock is a 5-dial lock?