SOLUTION: How many different license plates are possible if there are four letters and two digits (0 through 9) on each plate and no repetition of either is allowed?

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Question 1165886: How many different license plates are possible if there are four letters and two digits (0 through 9) on each plate and no repetition of either is allowed?
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
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There is one  VERY  IMPORTANT  moment,  which is  MISSED  in the problem's formulation.

In real life,  the letters in license plates usually are located on some fixed  (assigned) positions,
and the digit occupy the remaining positions.

The problem is  SILENT  about it,  which makes everything very  QUESTIONABLE  and  UNCERTAINT.

To be posed correctly,  the problem  EITHER  must say that the letters may occupy any  4  arbitrary positions,
OR are fixed in some  4  assigned positions.

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I just see the  SECOND  problem in a row posed  DEFECTIVELY.

It forces me to start thinking  what is the source  of these/such problems.



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How many different license plates are possible if there are four letters and two digits (0 through 9) on each plate and no repetition of either is allowed?
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The 4 letters (not case sensitive) ---> 26*25*24*23
The 2 digits ---> 10*9
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Overall, it's 26*25*24*23*10*9
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Some states (in the US) and other countries use various combinations w/o either letters or numbers being in a certain position.
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I had CG3B101 on a vehicle. Now its HHZ9PH.