Fundamental Principle of Counting Problem

  • Thread starter LisaL
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Homework Statement



A license plate has three letters followed by three numbers. Suppose the digits from 0...9 can be used, except all three digits cannot be zero, and that any letter from A-Z with repeats can be used. How many plates are possible?

Homework Equations



My question is on the 0. Does this mean NONE can be used or only TWO?

The Attempt at a Solution

I was marked wrong for the following:

I set up as 26 x 26 x 26 x 10 x 10 x 9 = 15,818,400

What is the correct way to set up this problem?

Thanks!
 

Answers and Replies

  • #2
vela
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Ignore the letters for now. If you could have 3 digits with no restrictions, how many numbers can you form? Now if you exclude the possibility of all three being zeros, how many do you have left?
 
  • #3
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Ignore the letters for now. If you could have 3 digits with no restrictions, how many numbers can you form? Now if you exclude the possibility of all three being zeros, how many do you have left?
OK, your point is made. The numbers 000 to 999 not including 000 total nine hundred and ninety nine. On the other hand 10x10x9 seems like it ought to work.
 

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