how many license plates are possible if four letters are to be followed by two digits?

Question

counting outcomes

Answer 1

Assuming you can use the letters and numbers again once they have already been used (i.e., if the first letter of the license plate is a B, you are able to use B again for any/some/all of the other three letters), then you just have to think about how many possibilities there are for each space of the license plate. For the first space, the only possibilities are all of the letters of the alphabet. That would be 26. The same holds true for the next 3 spaces (26 possibilities for each of them). Then for the 5th space, the only possibilities are digits. There are 10 digits (0-9). Same thing for the last space on the license plate. The total amount of license plates are figured out by multiplying each space together. So the answer is computed as: 26x26x26x26x10x10. Therefore, there are 45,697,600 possible license plates given the constraints in the question.

 

If you have any questions, feel free to reach out to me. And if you can't re-use the letters and numbers you previously used, then the answer is similar, but you need to think about it a little differently. I am happy to explain that to you. I hope this helps.

Answer 2

To be pedantic, you will note that certain letters can not be used on a License plate as this causes some confusion for instance the letter I and the number 1 cannot be distinguished.  Similarly the letter O and Q are not used for being to similar to the number 0.  So this changes the number of combinations, by quite a bit, the methodology used before was correct so the answer is (23^4) * (10^2) (where ^ denotes raised to the power of and * multiplication).  The answer is thus reduced to 27,984,100 (a little under under 28 Mio).  This would still be an overstatement certain combinations for instance would not be permitted least they cause offense or the impression for instance that the vehicle is affiliated with certain services (for instance the police).  

Comparing this to the population of individual states and an estimate of registered vehicles per person would determine if this was a viable basis for a state licensing system.  Looking at the increase over time of vehicle registrations in a state compare withthe number of combinations currently in use would alllow you to determine how many years before the system may longer be viable.