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:
[tex]n = \frac{5!}{(5-5)!}\\ n=5*4*3*2*1\\n=120\ ways[/tex]
The number of possible outcomes for the first 5 places is given by the permutation of 13 horses in the first five positions:
[tex]N = \frac{13!}{(13-5)!}\\ N=13*12*11*10*9\\N=154,440\ ways[/tex]
The probability that those five horses finish first, second, third, fourth and fifth is:
[tex]P=\frac{120}{154,440}\\ P=0.000777[/tex]
