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A license plate in a certain state consists of three digits, not necessarily distinct, and three letters, also not necessarily distinct. These six characters may appear in any order, except that no two letters can be next to each other. How many distinct plates?

 Aug 2, 2021
 #1
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Letter combos  = 26 x 26 x 26

can occupy two positions (to remain separated)

   like this    x o x o x o       or   o x o x o x

the other three can be the number combos   10 x 10 x 10 = 1000

 

26 x 26 x 26 x 2        x    1000 = ____________ combos

 Aug 2, 2021

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