Answer to POW #6:

You have a 1/6 chance of choosing your cards in alphabetical order.

The easy way to see this is to notice that, given any three cards from the deck, there are six ways to arrange the cards -- only one of which is in alphabetical order.

The more, um, detailed way to see this is as follows. There is only one way to start with the 24th letter and get three cards in alphabetical order (XYZ). There are 3 ways to start with the 23rd letter and have cards in order (WXY, WXZ, and WYZ). If you continue this pattern you will see that there number of ways to have three cards in order starting from the nth letter is the sum of the integers from 1 to 26-(n+1). Adding up all these possibilities, we arrive at 2,600 ways to choose three cards in alphabetical order. Since there are (26)(25)(24) = 15,600 ways to choose the cards in ANY order, this means there is a 15,600/2,600 = 1/6 chance of choosing the cards in alphabetical order.

Source: Adapted from a problem by Richard Neal, The Problem Solving Competition