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Question

The format for automobile license plates in Georgia before 2000 was 3 numbers followed by 3 letters (example: 123 ABC). How many different license plates in this format can there be?

Answer 1

There are 10 numbers (0 - 9) available for the first spot on the license plate as there are for the next two spots making a total of 10 x 10 x 10 = 1000 or 10^3 different combinations (or think of it as 000 to 999 combinations).  

 

Then there are 26 letters for the first letter placement as there are for the next two placements for a total of 26 x 26 x26 or 26^3 different combinations.

 

Combining both terms, there is a total of 10^3 x 26^3 = 26^3 x 1000 = 17,576 x 1000 = 17,576,000 different license plates can be possible