Chapter 8.1, Problem 71E

Exercises 69–72 use counting arguments from the preceding chapter.

Horse Races The seven contenders in the fifth horse race at Aqueduct on February 18, 2002, were Pipe Bomb, Expect a Ship, All That Magic, Electoral College, Celera, Cliff Glider, and Inca Halo.⁸ You are interested in the first three places (winner, second place, and third place) for the race.

a. Find the cardinality $n\left(S\right)$ of the sample space S of all possible finishes of the race. (A finish for the race consists of a first, a second, and a third place winner.)

b. Let E be the event that Electoral College is in second or third place, and let F be the event that Celera is the winner. Express the event $E\cap F$ in words, and find its cardinality.