Question

A horse race has 10 entries and one person owns 3 of those horses. Assuming that there are no ties, what is the probability that those horses finish 1st, 2nd, and 3rd (regardless of order)?

1) 1/120
2) 1/210
3) 1/252
4) 1/504

Answer 1

The probability that the three horses owned by a person finish 1st, 2nd, and 3rd in a horse race with 10 entries is 1/504.

Step-by-step explanation:

To find the probability that the three horses owned by the person finish 1st, 2nd, and 3rd (regardless of order), we can use the concept of combinations. There are 10 entries in total, and the person owns 3 of them. So, the number of ways we can choose 3 horses out of the 10 is given by the combination formula - C(10, 3) = 10! / (3! * (10-3)!).

Simplifying the expression, we have C(10, 3) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120.

Since there are 120 ways for the person's horses to finish 1st, 2nd, and 3rd, regardless of order, and we have a total of 10! ways for all the entries to finish, the probability is 120/10! = 1/504. Therefore, the correct option is 4) 1/504.