Question

A witness to a hit-and-run accident told the police that the license number contained the letters RLH followed by 3 digits, the first of which was a 5. If the witness cannot recall the last 2 digits, but is certain that all 3 digits are different, find the maximum number of automobile registrations that the police may have to check.

Answer 1

Since digits are different, available digits are 0,1,2,3,4,6,7,8,9( as 5 is already used)

Number of available digits = 9

2nd digit can be any of the above 9 digits

3rd digit can be any of the remaining 8 digits

hence police have to check $9 \times 8=72$ registrations