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On the island of Mumble, the Mumblian alphabet has only 5 letters, and every word in the Mumblian language has no more than 3 letters in it. How many words are possible? (A word can use a letter more than once, but 0 letters does not count as a word.)

tertre  Mar 23, 2017
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 #1
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There's an equation to this... l just can't put my finger on it.

HighSchoolCalculus  Mar 23, 2017
 #2
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The work can be 1,2 or 3 letters long.

 

If it is 1 letter then there are 5 choices

 

If it is 2 letters then there are 5 choices for the first letter and then 5 choices for the second letter. 

   That is 5*5 = 25 posibilities

 

If it is 3 letters then there are 5 choices for the first letter and then 5 choices for the second letter and 5 for the third

   That is 5*5*5 = 125 posibilities

 

So that makes

5+25+125 = 155  possible words    laugh

Melody  Mar 23, 2017

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