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?

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(52858) (Show Source): You can put this solution on YOUR website!
.

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) (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.

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