In a 16 horse race, what is the probability of choosing the winning trifecta? (Disregard odds on horses)

permutations of 16 taken 3 at a time

(order matters so permutations)
16!/[(16-3)!]

16!/[ 13! ]

16*15*14

3360 possible groups of 3 out of those 16
1/3360 = .000297 forget it unless you know a lot about the particular horses :) !

Ah, the thrilling world of horse racing! Well, if we disregard the odds on horses, we're left with pure randomness. In a 16-horse race, there are (16 choose 3) possible trifecta outcomes, which is equal to 560. So, the probability of choosing the winning trifecta purely by chance is 1 in 560. However, if you're relying on your clown instincts to make the picks, who knows, maybe your chances of success increase exponentially! 🤡

To calculate the probability of choosing the winning trifecta in a 16 horse race, we need to determine the number of possible outcomes for the winning trifecta and divide that by the total number of possible outcomes.

In a trifecta bet, you need to correctly pick the horses that will finish first, second, and third, in the exact order.

To determine the number of possible outcomes for the winning trifecta, we calculate the number of choices for each position:

There are 16 horses that can finish first.
Once the first horse is chosen, there are 15 remaining horses that can finish second.
Once the first two horses are chosen, there are 14 remaining horses that can finish third.

So the number of possible outcomes for the winning trifecta is 16 * 15 * 14 = 3,360.

Now, let's calculate the total number of possible outcomes in the race. Since there are 16 horses, any of the 16 horses can finish first, any of the remaining 15 horses can finish second, and any of the remaining 14 horses can finish third.

The total number of possible outcomes is 16 * 15 * 14 = 3,360.

Finally, we can calculate the probability of choosing the winning trifecta by dividing the number of possible outcomes for the winning trifecta by the total number of possible outcomes:

Probability = (Number of possible outcomes for the winning trifecta) / (Total number of possible outcomes) = 3,360 / 3,360 = 1 / 1 = 1.

Therefore, the probability of choosing the winning trifecta in a 16 horse race is 1, or 100%.

To calculate the probability of choosing the winning trifecta in a 16 horse race, we need to determine the number of possible outcomes and the number of favorable outcomes.

In a trifecta bet, you are selecting the first, second, and third place finishers in the correct order. Let's break down the calculation step-by-step:

Step 1: Determine the number of possible outcomes
In a 16 horse race, there are 16 choices for the first place, 15 choices for the second place (since one horse has already been chosen for the first place), and 14 choices for the third place (since two horses have already been chosen for the first and second place). Therefore, the number of possible outcomes is:

16 * 15 * 14 = 3,360

Step 2: Determine the number of favorable outcomes
There is only one winning trifecta combination in the race, which consists of choosing the first, second, and third place finishers in the correct order. Therefore, the number of favorable outcomes is:

1

Step 3: Calculate the probability
The probability is calculated by dividing the number of favorable outcomes by the number of possible outcomes. In this case:

Probability = Number of Favorable Outcomes / Number of Possible Outcomes

Probability = 1 / 3,360

Therefore, the probability of choosing the winning trifecta in a 16 horse race, disregarding odds on horses, is approximately 0.000297 or 0.0297%.

Please note that this calculation assumes all horses have an equal chance of winning, and it disregards any external factors or odds that may impact the race.