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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.)

Logic  Oct 25, 2018
 #1
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Okay.

 

Let A, B, C, D, and E stand for the five letters of the Mumblian alphabet.

 

Each word can be from 1-3 letters long, and letters can repeat.

 

Okay. Lets start with the words with 1 letter in them.

 

There are \(\boxed {5}\) possibilites of this.

 

Next up, the words with 2 letters in them.

 

There are \(5 * 5 = \boxed {25}\) possible 2 letter words.

 

Last, the words with 3 letters in them

 

There are \(5 * 5 * 5 = \boxed {125}\) possible 3 letter words.

 

There are a total of \(5 + 25 + 125 = \boxed{\boxed{155}}\) total words possible.

KnockOut  Oct 26, 2018

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