A horse race has 13 entries Assuming that there are no ties

A horse race has 13 entries. Assuming that there are no ties, what is the probability that the four horses owned by one person finish first, second, third and fourth?

The probability that the four horses finish first, second, third, and fourth is ___

Solution

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 4/13
The probability that any of the remaining 3 horses finishes second is 3/12
The probability that any of the remaining 2 horses finishes third is 2/11
And the probability that the last horse owned by this person finishes fourth is 1/10

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

4/13 * 3/12 * 2/11 * 1/10

= 4*3*2*1 / (13*12*11*10)

= 1/(13*11*5)

= 1 / 715 Ans