Question

A horse 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)

Answer 1

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