In Example 4.31 on page 211, we considered exacta wagering in horse racing. Two similar wagers are the quinella and the trifecta. In a quinella wager, the bettor picks the two horses that he or she believes will finish first and second, but not in a specified order. In a trifecta wager, the bettor picks the three horses he or she thinks will finish first, second, and third in a specified order. For a 12-horse race,
a. How many different quinella wagers are there?
b. How many different trifecta wagers are there?
c. Repeat parts (a) and (b) for an 8-horse race.