Question

Since 2009, all standard license plates issued in Guam have consisted of 2 letters (encoding the vehicle owner's village) followed by 4 numerical digits (each from 0 through 9). A witness to a hit and run accident reports to police that the two letters of the offending vehicle's plate were either HG or YG. The first numerical digit was a 3, 6, or 8. Each of the remaining 3 numerical digits was odd. How many possible Guam license plates meet this description?

Answer 1

750 license plates meet this description.

Explanation:

We have to find all possible 4-digit numbers that start with 3, 6 or 8 and the other 3 digits are odd. The digits can be repeated.

For the first digit we have 3 options (3,6,8) and for the other digits we have 5 options (1,3,5,7,9).

Therefore, the total of options we have are 3x5x5x5 = 375 different numbers with this characteristics.

Finally we can pair these numbers with HG or YG, therefore we have to multiply this number by two. 375 x 2 = 750.

So we can conclude that 750 plates meet this description.