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# How Many Trifecta Combinations Can You Have With 24 Horses?

A trifecta bet is a type of horse racing wager in which the bettor must select the first three finishers in a race in the exact order. It is a difficult wager to win, but the payouts can be quite large.

## What is the Difference Between a Trifecta and a Boxed Trifecta?

A trifecta is a type of horse racing wager in which the bettor must select the first three finishers in a race in the exact order. A boxed trifecta is a type of horse racing wager in which the bettor must select the first three finishers in a race in any order. With a boxed trifecta, the bettor has more flexibility in the order in which the horses finish, but the cost of the bet is higher than with a traditional trifecta.

## How Many Trifecta Combinations Can You Have with 24 Horses?

When it comes to trifecta wagers, the number of possible combinations can be quite large, depending on the number of horses in the race. If there are 24 horses in the race, there will be 1,639,840 possible trifecta combinations.

### Calculating the Number of Possible Trifecta Combinations with 24 Horses

The number of possible trifecta combinations with 24 horses can be calculated using the formula:

Number of Combinations = n! / ( n – r )! r!

Where:

• n = number of horses in the race
• r = number of horses required to finish in the exact order (in the case of a trifecta, this is 3)

Using this formula, the number of possible trifecta combinations with 24 horses can be calculated as follows:

Number of Combinations = 24! / ( 24 – 3 )! 3! = 1,639,840

### Calculating the Number of Possible Boxed Trifecta Combinations with 24 Horses

The number of possible boxed trifecta combinations with 24 horses can be calculated using the formula:

Number of Combinations = n^r

Where:

• n = number of horses in the race
• r = number of horses required to finish in any order (in the case of a boxed trifecta, this is 3)
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Using this formula, the number of possible boxed trifecta combinations with 24 horses can be calculated as follows:

Number of Combinations = 24^3 = 17,576

## What Are the Odds of Winning a Trifecta or Boxed Trifecta with 24 Horses?

The odds of winning a trifecta or boxed trifecta with 24 horses depend on the number of possible combinations and the amount of money wagered.

### Odds of Winning a Trifecta with 24 Horses

The odds of winning a trifecta with 24 horses can be calculated using the following formula:

Odds of Winning = (1 / Number of Combinations) * (Amount of Money Wagered)

Using this formula, the odds of winning a trifecta with 24 horses can be calculated as follows:

Odds of Winning = (1 / 1,639,840) * (\$1) = 0.00000061

### Odds of Winning a Boxed Trifecta with 24 Horses

The odds of winning a boxed trifecta with 24 horses can be calculated using the following formula:

Odds of Winning = (1 / Number of Combinations) * (Amount of Money Wagered)

Using this formula, the odds of winning a boxed trifecta with 24 horses can be calculated as follows:

Odds of Winning = (1 / 17,576) * (\$1) = 0.0000567

## What Are the Payouts for Trifecta and Boxed Trifecta Bets with 24 Horses?

The payouts for trifecta and boxed trifecta bets with 24 horses depend on the number of possible combinations, the amount of money wagered, and the takeout rate.

### Payouts for Trifecta Bets with 24 Horses

The payouts for trifecta bets with 24 horses can be calculated using the following formula:

Payout = (Number of Combinations / Amount of Money Wagered) * (Takeout Rate)

Using this formula, the payouts for trifecta bets with 24 horses can be calculated as follows:

Payout = (1,639,840 / \$1) * (0.15) = \$245,976

### Payouts for Boxed Trifecta Bets with 24 Horses

The payouts for boxed trifecta bets with 24 horses can be calculated using the following formula:

Payout = (Number of Combinations / Amount of Money Wagered) * (Takeout Rate)

Using this formula, the payouts for boxed trifecta bets with 24 horses can be calculated as follows:

Payout = (17,576 / \$1) * (0.15) = \$2,636

## Conclusion

Trifecta and boxed trifecta bets can be quite lucrative, especially when there are 24 horses in the race. There are 1,639,840 possible trifecta combinations with 24 horses, and 17,576 possible boxed trifecta combinations with 24 horses. The odds of winning a trifecta or boxed trifecta with 24 horses are 0.00000061 and 0.0000567, respectively. The payouts for trifecta and boxed trifecta bets with 24 horses are \$245,976 and \$2,636, respectively.