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The inhabitants of the island of Jumble use the standard Roman alphabet (26 letters, A through Z). Each word in their language is 3 letters, and for some reason, they insist that all words contain the letter A at least once. How many 3-letter words are possible?

gueesstt  Apr 22, 2018
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The A can appear in any one of 3 positions when it is used once

And there are 25 * 25  posiibilities  for the other two positions

So..... C( 3, 1) * 25^2    = 1875      

 

When the word has 2 A's....they can appear in any two of the three positions

And the the other position can be filled in 25 ways

So  C(3,2) * 25  =  75    

 

And  only one word has three A's  

 

So...the total possible words  =   1875  + 75  + 1  =    1951

 

 

cool cool cool

CPhill  Apr 22, 2018

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