Rachel's Problem

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!

Snowman

Stage: 4 Challenge Level:
 All the words in the Snowman language consist of exactly seven letters formed from the letters {s, no, wm, an} arranged in some order where the paired letters cannot be separated. For example snonono'' and sssanwm'' are words in the language but sssmwan'' and sssawmn'' are not. How many words are there in the Snowman language?