POW #6: Alphabetical Cards

You have a deck of 26 cards, each labeled with one of the 26 letters of the alphabet. (Each letter appears on exactly one card.) Suppose you choose three cards at random, one at a time, from this deck. What is the probability that you choose your cards in alphabetical order? (For example, choosing G, then R, then X is in alphabetical order, but choosing R, then G, then X is not.) Give an exact answer, not an approximation, and show clearly how you arrived at your answer.

Return to Laura Taalman, Burruss 127, by 3/17/04.
Include your name and email address with your solution.