Question

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

Answer 1

Hello there.

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

=0.000999

Answer 2

The key here is that there is no requirement that any specific horse of the four horses finishes in a particular place of the first four places.

The probability that any of the 4 horses finishes first is 4/14
The probability that any of the remaining 3 horses finishes second is 3/13
The probability that any of the remaining 2 horses finishes third is 2/12
And the probability that the last horse owned by this person finishes fourth is 1/11

Now multiply the probability to obtain the overall probability of these 4 four events occurring and you get

4/14 * 3/13 * 2/12 * 1/11 = 4*3*2*1 / (14*13*12*11)