Question

A horse race has 13 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, second, third, fourth and fifth?

Answer 1

Answer:

0.000777

Step-by-step explanation:

The number of possibilities that the 5 horses can finish in the first 5 spots is given by the permutation of those five horses in the first five positions:

$n = \frac{5!}{(5-5)!}\\ n=5*4*3*2*1\\n=120\ ways$

The number of possible outcomes for the first 5 places is given by the permutation of 13 horses in the first five positions:

$N = \frac{13!}{(13-5)!}\\ N=13*12*11*10*9\\N=154,440\ ways$

The probability that those five horses finish first, second, third, fourth and fifth is:

$P=\frac{120}{154,440}\\ P=0.000777$