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 sixteen 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 have the same chance to win.)

Step 1 ：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 sixteen 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 have the same chance to win.)

Step 2 ：The total number of possible outcomes is the number of ways to arrange 16 horses in the first three places, which is a permutation of 16 items taken 3 at a time. This can be calculated as \(16 \times 15 \times 14 = 3360\).

Step 3 ：The number of successful outcomes is the number of ways to arrange the 3 horses you selected in the first three places, which is a permutation of 3 items taken 3 at a time. This can be calculated as \(3 \times 2 \times 1 = 6\).

Step 4 ：The probability of winning is the ratio of successful outcomes to total outcomes. This can be calculated as \(\frac{6}{3360} = 0.0017857142857142857\).

Step 5 ：Final Answer: The probability that you will win the trifecta is approximately \(\boxed{0.00179}\).