When gambling on any type of racing, a trifecta bet is one where you need to pic

Question

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. If a total of 59 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?

Explanation / Answer

A)

As order matters, we use permutations.

Hence, there are

59P3 = 195054 ways [ANSWER]

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b)

As order does not matter, we use combinations.

Hence, there are

59C3 = 32509 ways [ANSWER]

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