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"Trifecta" Horse race. If 8 horses are entered into a race, how many tickets must you buy in order to gurantee?

"Trifecta" Horse race. If 8 horses are entered into a race, how many tickets must you buy in order to gurantee that one of them will be a trifecta winner? How do you solve this? Do you need a scientific calculator?

Public Comments

1. It's more than 8. I'm just too lazy to try to answer this. You don't need a scientific calculator. It's not that hard. In trifecta races, the bettor must select the first three finishers in exact order.
2. If it's a $1 bet -- the answer is $336. That is 8 times 7 times 6. Eight horses could finish 1st. Then with one of them finishing 1st, there are 7 other possibilities that can finish 2nd, and so forth
3. There are 336 combinations of the 8 horses coming in the top 3 placings. Think about it this way. You want one horse to win... then one horse to come second. That's two horses out of the 8, leaving 6 to come in third. Illustration: 1st: A 2nd: B 3rd: C D E F G H So for A to win and B to come second, there's 6 combinations. Now we need to do that for all the other horses coming in 2nd. Since we know A will win, we need B, C, D, E, F, G, and H to come 2nd... that's 7 horses... so we multiply 6 (the answer from our original question) times 7 (the number of horses who could come 2nd), and we end up with 42. Illustration A C B D E F G H A D B C E F G H A E B C D F G H etc. Now we need to multiply that by all the horses in the race (because any one of them can win). There's 8 horses, times the 42 combinations of the results under them, and you get 336. This method works for any exotic bet in horse racing... exacta, trifecta, superfecta... you start with the number of horses, then multiply that by one less than the number of horses for an exacta (only one multiplication because there's only two placings), then one less than that for a trifecta (two multiplications because there's 3 placings), and then one less than that for a superfecta (3 multiplcations because there's 4 placings). Is this a math problem or a handicapping question? If you're just doing math homework, this won't help you, but if you're a learning handicapper, I like to use exotic wager calculators as a simple easy way of figuring out how much each bet will cost. Here's a link to one: http://www.horsehats.com/exotic-wager-calculator.html