Question 1134057: In a certain region all license plates are composed of three letters followed by three numbers, or three numbers followed by three letters. The only restriction is that zero can never be the first of the three numbers if the three numbers come first. Find how many license plates are possible.
Found 2 solutions by Glaviolette, ikleyn:
Answer by Glaviolette(140)   (Show Source):
You can put this solution on YOUR website! The first space can either be a number (other than 0) or a letter, therefore, there are 35 options (26 + 9). If the first space is filled with a number, there are then 10 options for the second space and 10 for the third space (keeping them numbers). The last 3 spaces would be letters, 26 options for each. Using the counting principle, these values are multiplied...
35*10*10*26*26*26 = 61516000
If the first space was filled with a letter, there are 26 options for space 2, 26 for space three. Then switching to numbers, 10 options for each of the remaining 3 spaces.
35*26*26*10*10*10 = 23660000
For a total of 85176000 possible license plates. Wow, that was fun
Answer by ikleyn(52754)  (Show Source):
You can put this solution on YOUR website! .
In a certain region all license plates are composed of three letters followed by three numbers,
or three numbers followed by three letters. The only restriction is that zero can never be
the first of the three numbers if the three numbers come first.
Find how many license plates are possible.
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The solution in the post by Glaviolette is incorrect.
So I came to bring a correct solution in three simple clear steps.
(1) if 3 digits go first, followed by 3 letters, with the imposed restrictions,
then the number of plates is 9*10*10*26*26*26 = 15818400.
(2) if 3 letters go first, followed by 3 digits (no restrictions in this case)
then the number of plates is 26*26*26*10*10*10 = 17576000.
(3) The answer is the sum of these numbers 15818400 + 17576000 = 33394400.
Solved.
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