Suppose the California DMV comes up with a new license

Suppose the California DMV comes up with a new license plate with a special serial number format. This serial number format consists of only 3 letters: first two being a digit (0 to 9) and last one being an English uppercase letter (A to Z). Each serial number is randomly generated when issued.

(a) Suppose Alice and Bob apply for this new license plate. What is the probability that both of them receive the same plate number?

(b) Suppose the California DMV wants to ensure that the probability that at least two license plates have the same number is less than 1%. What is the maximum number of this type of license plates that they can issue?

(c) Suppose the DMV wants to issue exactly 50 license plates. How many More DIGITS should be added at the end of this serial number format in order to ensure that the probability that at least two license plates have the same number is still less than 1%.