C Question 13, 13.1.57
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In horse racing, a trifecta is a race in which you must pick the first-, second-, and third-place winners in their proper order to win a payoff if thirteen horses are racing. and you randomly select three as your bet in the trifecta, what is the probability that you will win? (Assume that all horses nave the same chance to win)

What is the probability that you will win?

Step 1 ：The problem is asking for the probability of winning a trifecta bet in a horse race with 13 horses. A trifecta bet requires correctly predicting the first, second, and third place horses in the correct order.

Step 2 ：Since the order matters, this is a permutation problem. The total number of possible outcomes is the number of ways to arrange 3 horses out of 13, which is a permutation of 13 items taken 3 at a time, denoted as P(13,3).

Step 3 ：The number of successful outcomes is 1, because there is only one correct order of the first, second, and third place horses.

Step 4 ：The probability of a successful outcome is the number of successful outcomes divided by the total number of outcomes.

Step 5 ：Let's calculate this probability. The total number of outcomes is 1716 and the number of successful outcomes is 1.

Step 6 ：So, the probability is \(\frac{1}{1716}\) which is approximately 0.0005827505827505828.

Step 7 ：Final Answer: The probability that you will win the trifecta bet is approximately \(\boxed{0.0005827505827505828}\).