a license plate in the country kerrania consists of 4 digits followed by two letters . the letters a , b , and c are used only by government vehicles while the letters d through z are used by non - government vehicles . kerrania ' s intelligence agency has recently captured a message from the country gonzalia indicating that an electronic transmitter has been installed in a kerrania government vehicle with a license plate starting with 79 . if it takes the police 10 minutes to inspect each vehicle , what is the probability that the police will find the transmitter within 3 hours ?	Choose the correct choice from the following answers.
A) 18 / 79 B) 1 / 6 C) 1 / 25 D) 1 / 50 E) 1 / 900

Rationale: if it takes 10 minutes to inspect one vehicle , the # of vehicles that can be inspected in 3 hours ( 180 minutes ) = 180 / 10 = 18 . hence , for calculating the probability that the police will find the transmitter within three hours , the favorable cases = 18 . now , we need to figure out the total # of cases . the total # of cases = total # of such cars possible . the details given about the car is that it starts with 79 , which leaves 2 more digits , both of which can be filled by all 10 numbers ( 0 - 9 ) . in addition , we have 3 letters , each of which can be filled by any from the set { a , b , c } . hence the total # of such cars possible = 10 * 10 * 3 * 3 = 900 so , the probability that the police will find the transmitter within three hours = 18 / 900 = 1 / 50 . option d
Answer: D