Sometimes, order is important.
Counting all the possible ways in which you can order things is time consuming, but the trouble is, this sort of information is crucial for calculating some probabilities. In this chapter, we’ll show you a quick way of deriving this sort of information without you having to figure out what all of the possible outcomes are. Come with us and we’ll show you how to count the possibilities.
One of the biggest sporting events in Statsville is the Statsville Derby. Horses and jockeys travel from far and wide to see which horse can complete the track in the shortest time, and you can place bets on the outcome of each race. There’s a lot of money to be made if you can predict the top three finishers in each race.
The opening set of races is for rookies, horses that have never competed in a race before. This time, no statistics are available for previous races to help you anticipate how well each horse will do. This means you have to assume that each horse has an equal chance of winning, and it all comes down to simple probability.
The first race of the day, the three-horse race, is just about to begin, and the Derby is taking bets. You have $500 of winnings from Fat Dan’s Casino to spend ...