Question

a horse race has 11 entries and one person owns 4 of those horses. assuming that there are no ties, what is the probability that those four horses finish first, second, third, and fourth (regardless of order)?

the probability that the four horses finish first, second, third, and fourth is .
(round to four decimal places as needed.)

Explanation:

Identify total outcomes

Using the Combinatorics knowledge point

$$ N = \binom{11}{4} = \frac{11 \times 10 \times 9 \times 8}{4 \times 3 \times 2 \times 1} = 330 $$

Identify favorable outcomes

Using the Combinatorics knowledge point

$$ n = \binom{4}{4} = 1 $$

Calculate probability

Using the Classical Probability knowledge point

$$ P = \frac{n}{N} = \frac{1}{330} \approx 0.0030303... $$

Round to four decimal places

Using the Classical Probability knowledge point

$$ P \approx 0.0030 $$

Answer:

A horse race has 11 entries and one person owns 4 of those horses. Assuming that there are no ties, what is the probability that those four horses finish first, second, third, and fourth (regardless of order)?

The probability that the four horses finish first, second, third, and fourth is <blank>0.0030</blank>
(Round to four decimal places as needed.)