San Francisco Scramble

The Problem

The San Francisco Chronicle has a word game where all the letters are scrambled up and you have to figure out what the word is. Imagine that a scrambled word is 5 characters long:

1. How many possible solutions are there?
2. What if we know which 5 letters are being used?
3. Develop an algorithm to solve the word.

The Solution

This is a fantastic way to phrase the question. There are 265 solutions (each letter can be one of 26 possible values). If we know which five letters are being used there are 55 possible solutions.