The Petersonian alphabet consists of the 5 letters: O, R, Z, S, T. Any sequence of 1-8 letters is a valid word in this language (including words with repeated letters). How many different words does the Petersonian language contain?
+137 $5^8 + 5^7 + 5^6 + 5^5 + 5^4 + 5^3 + 5^2 + 5^1 = \boxed{488280}$ words, as there can be words with 1-7 letters as well.
