A license plate in the country Kerrania consists of four 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 5 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours? Choose the most appropriate option
A) 18/79  B) 1/6  C) 1/25  D) 1/50  E) 1/900
If it takes 5 minutes to inspect one vehicle, the # of vehicles that can be inspected in 3 hours (180 minutes) = 180/5= 
<gadget id="calculator">180/5</gadget>
<output>36</output>
36. Hence, for calculating the probability that the police will find the transmitter within three hours, the favorable cases= 36. 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= 
<gadget id="calculator">10*10*3*3</gadget>
<output>900</output>
900   So, the probability that the police will find the transmitter within three hours= 36/900 = 1/25. Option 1/25
<result>C</result>
A license plate in the country Kerrania consists of four 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 5 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?