a horse race has 11 entries, assuming that their are no ties what is the probability that four horses owned by one person finish first second third and fourth
Please tell us how many owners there are in total, and how many horses are owned by each of them.
that is the only information given
assume that 7 horses are owned by 7 different owners and the other 4 are owned by the same person
To calculate the probability of four specific horses owned by one person finishing first, second, third, and fourth in a horse race with 11 entries, we first need to determine the total number of possible outcomes.
The first position can be occupied by any of the 11 horses, so there are 11 options. Once that position is filled, there are 10 horses remaining for the second position, 9 for the third position, and 8 for the fourth position.
Thus, the total number of possible outcomes is calculated as follows:
11 options for the first position × 10 options for the second position × 9 options for the third position × 8 options for the fourth position = 88,440 possible outcomes.
Next, we need to determine the number of favorable outcomes where the four specific horses owned by one person finish in the top four positions. Since it is given that the four horses owned by one person will occupy the top four positions, we don't need to worry about the specific order in which they finish.
There are 4 horses owned by one person, and since they must finish in the top four positions, we simply need to calculate how many possible arrangements or permutations exist for these 4 horses in the top four spots. This can be calculated as follows:
Number of permutations of 4 horses in the top four positions = 4 × 3 × 2 × 1 = 24 permutations.
Therefore, the number of favorable outcomes is 24.
Finally, to determine the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 24 / 88,440 ≈ 0.000271
Hence, the probability that four horses owned by one person finish first, second, third, and fourth in the given horse race is approximately 0.000271, or about 0.0271%.