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- Homework Statement
- A witness to a hit-and-run accident tells the police that the license plate of the car in the accident, which contains three letters followed by three digits, starts with the letter A and contains both the digits 1 and 2. How many different license plates can fit this description?

- Relevant Equations
- Counting

permutation(?) = P(n,r) = n!/(n-r)!

I have a question and searched about at google and found an answer which I don't make sure. If there is 26 letters and 10 digits;

my answer is:

first letter: 1 way(which is A)

second letter: 26 way

third letter: 26 way

first digit: 1 way(which is 1)

second digit 1 way(which is 2)

third digit: 10 way

So, I think 26x26x10 license plates can fit this description.

But the other guy had said:

in addition above statements: order three digits ; P(3,3), order three letters ; P(3,3) , thus 26x26x10xP(3,3)xP(3,3)

Which one is correct? Would you please tell how we should think?

edit: I add a photo above so new arrivals can know the drill easily .

my answer is:

first letter: 1 way(which is A)

second letter: 26 way

third letter: 26 way

first digit: 1 way(which is 1)

second digit 1 way(which is 2)

third digit: 10 way

So, I think 26x26x10 license plates can fit this description.

But the other guy had said:

in addition above statements: order three digits ; P(3,3), order three letters ; P(3,3) , thus 26x26x10xP(3,3)xP(3,3)

Which one is correct? Would you please tell how we should think?

edit: I add a photo above so new arrivals can know the drill easily .

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