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You have eight letter tiles: L, A, D, Y, G, A, G, A.  How many different three-letter words can you form from these tiles?

 May 9, 2020
 #1
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 L, A, D, Y, G, A, G, A

 

Will consider the 5 repeated letters as 2. So will have: 6 nPr 3 = 120. From that will subtract: 6 nCr 2 + 6 nCr 3. And will have 120 - 15 - 20 =85 permutations of 3-letters each as follows:

 

{A, A, A} | {A, A, D} | {A, A, G} | {A, A, L} | {A, A, Y} | {A, D, A} | {A, D, G} | {A, D, L} | {A, D, Y} | {A, G, A} | {A, G, D} | {A, G, G} | {A, G, L} | {A, G, Y} | {A, L, A} | {A, L, D} | {A, L, G} | {A, L, Y} | {A, Y, A} | {A, Y, D} | {A, Y, G} | {A, Y, L} | {D, A, A} | {D, A, G} | {D, A, L} | {D, A, Y} | {D, G, A} | {D, G, G} | {D, G, L} | {D, G, Y} | {D, L, A} | {D, L, G} | {D, L, Y} | {D, Y, A} | {D, Y, G} | {D, Y, L} | {G, A, A} | {G, A, D} | {G, A, G} | {G, A, L} | {G, A, Y} | {G, D, A} | {G, D, G} | {G, D, L} | {G, D, Y} | {G, G, A} | {G, G, D} | {G, G, L} | {G, G, Y} | {G, L, A} | {G, L, D} | {G, L, G} | {G, L, Y} | {G, Y, A} | {G, Y, D} | {G, Y, G} | {G, Y, L} | {L, A, A} | {L, A, D} | {L, A, G} | {L, A, Y} | {L, D, A} | {L, D, G} | {L, D, Y} | {L, G, A} | {L, G, D} | {L, G, G} | {L, G, Y} | {L, Y, A} | {L, Y, D} | {L, Y, G} | {Y, A, A} | {Y, A, D} | {Y, A, G} | {Y, A, L} | {Y, D, A} | {Y, D, G} | {Y, D, L} | {Y, G, A} | {Y, G, D} | {Y, G, G} | {Y, G, L} | {Y, L, A} | {Y, L, D} | {Y, L, G} (total: 85)

 May 9, 2020
 #2
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Then of course, it depends on whether the Guest's question is asking for just letter arrangements or actual words.

 

The question has some ambiguity on that.

 

Of course I have not done the question for myself and this is an untested suggestion.

hugomimihu  May 9, 2020

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