Question

1. A license plate must be 7 characters long: available characters are uppercase letters (26 possible letters for each spot), digits (0-9, so 10 possible numbers for each spot), and special characters!*-& and a blank space (5 possible special characters). A rental car company wants all of its cars' license plates to begin with 4 letters, then have 1 special character, and then 2 digits, e.g. "ABCD 68" is permissible, but "ABCD6 8" is not. a) How many different license plates are possible for a car belonging to this company? b) How many different license plates are possible for a car in this company if none of the digits may be repeated? (c) How many license plates are possible for a car in this company if no character (letters, special characters, or digits) can appear twice? (d) You rent a car from this company during an island vacation, but two days into your vacation the car is stolen. You need to file a police report, but you need to know the license plate of the car. You don't remember the whole license plate, but you do remember that the first four characters are, aptly, "FRIG," in that order. Because you just want to get back to sipping daiquiris on the beach, you decide to just take a random guess at the remaining characters and let the police deal with it. What is the probability that you guess correctly?

Answer 1

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Problem on classical probability, where the required probability is actually (favourable cases / total no. of cases).