In a horse race, a particular bet is won if you selected the two horses that finish first and second, and they can be selected in any order. A certain horse race had a field of 17 winning this bet if you randomly select the horses? The possibility of winning this bet when randomly selecting the horses is (Round to five decimal places as needed.)

To determine the probability of winning the bet by randomly selecting the first and second place horses in a race of 17 horses, we first need to consider that there are a total of \( C(17, 2) \) ways to choose 2 horses from the 17, which equals \( \frac{17 \times 16}{2} = 136 \) combinations of horses. Since the order in which the two selected horses finish matters (first and second), we multiply by 2! (the number of arrangements of the 2 horses), giving us \( 136 \times 2 = 272 \) total outcomes where any two horses finish in the first two positions. Now, since you cannot decide which horse wins first or second ahead of time, there is only 1 favorable outcome (the correct combination of horses). Therefore, the probability of winning the bet is: \[ P(\text{winning}) = \frac{\text{favorable outcomes}}{\text{total outcomes}} = \frac{1}{272} \] When calculated, this probability is approximately 0.00368. After rounding to five decimal places, the probability becomes 0.00368.