Question

Let’s suppose that Georgia wants to adopt a new license plate numbering system. The new license plates will be of the form X-NNNN-XX where N’s are numbers and X’s are letters. However, license plate numbers can’t begin or end with O and the 2nd # can’t be a 0.

How many different license plates are there under this system?

Answer 1

Answer: 146,250,000

==============================================

Step-by-step explanation:

For the first and last X, there are 25 choices. This is because there are 26 letters, but we can't use the letter O. The second to last X has 26 choices.

So far we have 25*26*25 = 16250 different permutations for the letter portion of the license plate.

Now onto the number portion. The first N can't be zero, but it can be any other positive single digit number. We have 9 choices for this slot. The other N's can be zero or any other positive single digit number. We have 10 choices for each of these slots.

So we have 9*10*10*10 = 9000 different permutations for the number portion of the license plate.

Overall, there are 16250*9000 = 146,250,000 different license plates that can be formed. This is a little bit over 146 million.

--------

If you want to do the all of the multiplication as one single step, then it might look like this:

25*9*10*10*10*26*25 = 146,250,000