When gambling on any type of racing a trifecta bet is one wh

   When gambling on any type of racing, a trifecta bet is one where you need to pick the first three finishers of the race in the exact order in order to win the bet and a boxed trifecta bet is one where you need to pick the first three finishers in the race in any order to win. In the 1960 Daytona 500 (which was the first NASCAR event to ever be televised), a total of 68 racers competed and if a person had decided to make a bet on the race: a) How many different possible trifecta bets could they have made? b) How many different possible boxed trifecta bets could they have made?

Solution

A)

As order matters here, then we use permutations. Hence, there are

#ways = 68P3 = 300696 ways [ANSWER]

***************

b)

As order does not matter here, we use combinations. Hence, there are

#ways = 68C3 = 50116 [ANSWER]