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

#2**+1 **

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

Melody
Mar 23, 2017