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How many 4-letter "words: are there in which no letter appears 3 or more times in a row?

 Apr 6, 2020
 #1
avatar+111329 
+2

Possible  4 letter  words  =  26^4

 

Possible  4 letter words  with all letters the  same  =  26

 

Possible  4 letter words  having three repeated letters  =  (choose  any letter to be repeated 3 times) * choose any  of  the other 25 letters * let  this last letter occupy either  the first or last position   = 26 * 25 * 2

 

So...possible 4 letter words  where  no word has a letter repeated  3 or  more times  = 

 

26^4  - 26  -  26 * 25 * 2 =

 

455,460

 

 

cool cool cool

 Apr 7, 2020
 #2
avatar+32 
+1

Oh, I see--we'd use the complementary counting method. Thanks! :)

Frooglie  Apr 7, 2020

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