Answer:
The required probability is 0.0004995
Step-by-step explanation:
Consider the provided information
There are 14 horses and one person owns 5 of those horses.
We need to find the number of ways in which 5 horses finish first, second , third, fourth, and fifth.
Each horse has the same probability of winning,
Therefore, the required probability is:
The probability that one of those 5 horses will be first is ![\frac{5}{14}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B14%7D)
Now we have 4 horses left,
Probability that out of remaining 4 horses one will be second is
.
The probability that out of remaining 3 horses one will be third is
.
The probability that out of remaining 2 horses one will be fourth is
.
The probability that out of remaining 1 horses one will be fifth is
.
Hence, the total probability is:
![\frac{5}{14}\times \frac{4}{13} \times \frac{3}{12} \times \frac{2}{11}\times \frac{1}{10}=0.0004995](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B14%7D%5Ctimes%20%5Cfrac%7B4%7D%7B13%7D%20%5Ctimes%20%5Cfrac%7B3%7D%7B12%7D%20%5Ctimes%20%5Cfrac%7B2%7D%7B11%7D%5Ctimes%20%5Cfrac%7B1%7D%7B10%7D%3D0.0004995)
Hence, the required probability is 0.0004995