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The question is: Given a licence plate that can have either 2 or 3 letters followed by either 2 or 3 numbers, how many different license plates can be printed.

My math is as such $(26^2 + 26^3)*(9^2+9^3)$ which comes to 14,784,120 but the book says the answer is 20,077,200. What am I doing wrong here?

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    @Debanjan: You are right. One reason I think license plates are used is to allow leading zeros.2010-11-11

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I got the same answer as the book: 20,077,200

And here's the equation: 27 * 26 * 26 * 11 * 10 * 10

Simply put, since the license plate can have 2 or 3 letters and 2 or 3 numbers, you can consider the first letter and first number to have extra one choice: the 'null' letter/number!

So the first letter can be A to Z or null: 27 choices

The second and third letters can be A to Z: 26 choices each

The first number can be 0 to 9 or null: 11 choices

The second and third letters can be 0 to 9: 10 choices each

Multiply them together to get 20077200.