EXAMPLE 1.5.8

There are 8 horses in a race. If all we are concerned with are the first, second and third place finishers (the trifecta), how many different orders of finish are possible?

SOLUTION

We are concerned with choosing three of the eight horses and arranging them according to which horse finishes first, which finishes second, and which finishes third. The number of ways to choose and arrange three things from a set of 8 things is P(8,3).

Assuming that the 8 horses are roughly equal in ability, the likelihood of a bettor winning the Trifecta is about 1 out of 336.