How many possible license plates are there without constraints?

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SUMMARY

The total number of possible license plates formatted as 3 digits, followed by 3 letters, and then 3 digits (123ABC123) without constraints is calculated using the counting principle. Each digit can range from 0 to 9, providing 10 options per digit, while each letter can be any of the 26 letters in the English alphabet. Therefore, the total combinations are calculated as 10^6 (for the digits) multiplied by 26^3 (for the letters), resulting in 1,000,000,000 possible license plates.

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Homework Statement


a license plate has 3mos then 3letters then 3nos(numbers) if there are no constraints
how many license plates are possible


Homework Equations


9x9x9x9x9x9x9(..maybe)


The Attempt at a Solution


The same as the one above, I am very confused.
 
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So, if I understand it correctly, the license plate is of the form 123ABC123. There are no constraints, that means the numbers don't need to be unique.

Think about it is a number of slots. In each slots you can put one of several possible values.

What if the license plate was just one number followed by one letter? Try to answer this simpler problem first, and then generalize.
 
I think by "9x9x9x..." you are referring to the "counting principle". Yes, that can be used here. However, if there are no constraints, so that any of the digits can be 0 to 9, there are 10 digits, not 9. And, of course, there are 26 letters.
 

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