Ahorse race has 14 entries and one person owns 5 of those horses. assuming that there are no ties, what is the probability that those five horses finish first comma second comma third comma fourth comma and fifth (regardless of order)

We know that
entries > 14 in total.
the owner has>  5 horses.

if each horse has the same probability of winning, then the probability that the owner's horses will come in first, second, third, fourth and fifth will be as follows: 
we have 5 spots. 

the probability that one of those 5 horses will be first is 5/14
the probability that one of the remaining 4 horses will be second is 4/13.
the probability that one of the remaining 3 horses will be third is 3/12.
the probability that one of the remaining 2 horses will be fourth is 2/11.
the probability that the remaining horse will be fifth is 1/10. 

the total probability is [5/14 * 4/13 *3/12 *2/11 *1/10]
(120/240240)=1/2002=0.0004995

the answer is 0.0004995

The vertex of the quadratic function is (1.5, -.75)