Question

The alphabet of a fictionary tribe consists of three letters: A, O and M. Any combination of no more than four of these letters is considered a word. How many words are does this tribe's language have?

Answer 1

120 different words

Explanation:

The max longest word has 4 letters

So the word can consist of 1 letter. The number of such wordds is 3 (A,O or M)

The word can consist also of 2 letters ( letters can be repeated in the word-

the word like AA or MM are possible). The number of such words is 3*3=9

The word can consist also of 3 letters ( letters can be repeated in the word-

the word like AMA or MMM are possible). The number of such words is 3*3*3=27

The word can consist also of 4 letters ( letters can be repeated in the word-

the word like AAAA or MAOM are possible). The number of such words is 3*3*3*3=81

So total number of words is 3+9+27+81=120