If it takes 10 minutes to inspect one vehicle, the number 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 number of cases = Total 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).
Given that vehicle to be found is government's , we have 3 letters, each of which can be filled by any from the set {A,B,C}. Hence the total number of such cars possible = 10*10*3*3 = 900

So, the probability that the police will find the transmitter in 3 hours
18/900 = 1/50. Option D

The license plate consists of 4 digits followed by 2 letters
The letters A, B, and C are used by government vehicles
The letters D and Z are used by non-government vehicles


The intelligence agency is looking for a license plate starting with 79. Hence, there are 2 unknown digits and 2 unknown letters.
It takes the police 10 minutes to search 1 car so in (3 * 60 = 180) minutes, they can search 180/10 = 18 cars


For 2 unknown digits, there are 10 possible digits from 0 to 9
For 2 unknown letters, there are 3 possible letters A, B, and C for government vehicles
Therefore, total possible plates = 10 * 10 * 3 * 3 = 900
The probability of finding the transmitter in 3 hours = 18/900
= 1/50


Answer = D