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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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    Think about how many digits you have? 9 or 10?2010-11-11
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    0s are for hippies.No actually thanks a lot, that explains it and I feel stupid yet again.2010-11-11
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    @Mark You have just insulted me. (Which means either of two things: I don't want to be a hippie but I like 0s, OR, I am a hippie and I don't like 0s. If the latter is true, then I am easily offended. But then would I be flaming? -- The power of logic.)2010-11-11
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    Is it only me or anybody else too thinks that it should be mentioned `that the repetitions of digits and alphabets are allowed`?2010-11-11
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    @Debanjan: More to the point, most places do not allow *any* letter in a license plate! Many places have no 'O's (easy to confuse with zeros), or I's (with 1s); or sometimes they avoid Q's (easy to confuse with Os)... (-: But here I think that the "repetitions allowed" is implicit if you about license plates.2010-11-11
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    @Arturo Magidin :Thanks, this kind of question (based on licence plates) is new to me, for example if the question is like this :`How many license plates can be made using either 3 digits followed by 3 letters or 3 letters followed by 3 digits?` then according to my understanding this should be $2*(26^3*10^3)$ .. am I correct ?2010-11-11
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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.