In a horse race with 6 horses, you make a bet by predicting the ranking of all 6 horses.

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In a horse race with 6 horses, you make a bet by predicting the ranking of all 6 horses. If you place your bet at random, what is the probability that you will get the first and second horse correct and in the correct order? Enter your answer as a simplified fraction. Provide your answer below: FEEDBACK SUBMIT

The Correct Answer and Explanation is:

To solve this problem, we need to determine the probability of selecting the first and second horses correctly and in the correct order out of 6 horses.

Step-by-step Breakdown:

  1. Total Possible Outcomes:
    When you place a bet on all 6 horses, you’re trying to predict the exact order in which they finish. There are 6 horses, so the total number of possible outcomes (or permutations) is given by: 6!=6×5×4×3×2×1=7206! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 7206!=6×5×4×3×2×1=720 So, there are 720 possible ways the 6 horses can finish the race.
  2. Correct First and Second Horses:
    Now, you are only concerned about the first and second horses being correct, and in the correct order. This means:
    • You must choose the correct horse to finish first.
    • You must then choose the correct horse to finish second from the remaining 5 horses.
    There are only one correct choice for the first horse, and once that choice is made, there is only one correct choice for the second horse. So, the number of favorable outcomes is 1 (correct first horse) × 1 (correct second horse) = 1.
  3. Probability Calculation:
    The probability of getting the first and second horses correct and in the correct order is the number of favorable outcomes divided by the total possible outcomes: Probability=1720\text{Probability} = \frac{1}{720}Probability=7201​

Conclusion:

The probability that you will get the first and second horses correct and in the correct order is:1720\boxed{\frac{1}{720}}7201​​

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