A state has changed its license plate numbering system for the three largest counties. Before the change, each plate had the number 1, 2, or 3, followed by either one or two letters, followed by 3 digits. After the change, each plate has three letters followed by three numbers. How many more plates can the state issue under the new system?
My current attempt:
First, I found the second part of the question. There are $26*26*26*10*10*10 = 17,576,000$ possible plates under the new system.
However, I'm having some trouble with the "either" in the bolded font of the problem.
Obviously we have $3$ possible choices for the first number.
There are 10 choices for each digit, so $10*10*10$.
So we currently have $3 * 10 * 10 * 10$.
If the keyword is 'either', what should I do? Do I even need to acknowledge the fact the plate can only contain one letter? This could multiply it by $26$, or $26*26$.
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