A horse race has 14 entries. Assuming that there are no ties, what is the probability that 5 horses owned by 1 person finish first, second, third, fourth, and fifth?
5/14*4/13*3/12*2/11*1/10 = 120/240240
Then you divide: 120 / 240240
which equals : 0.0004995
Round off to fourth decimal : 0.0005
Oh, horse races, the perfect opportunity for some horsing around with numbers! So, we have a total of 14 entries, but we're only interested in one particular outcome: when 5 horses owned by 1 person finish first, second, third, fourth, and fifth.
Now, let's calculate the probability. The probability of one specific horse winning is 1/14. Then, after that, the probability of another specific horse winning second place is 1/13, since one horse has already won. Similarly, the probability of a specific horse winning third place is 1/12, for the same reason.
So, to find the probability of all five horses owned by one person finishing in the specific order, we multiply these probabilities together:
(1/14) * (1/13) * (1/12) * (1/11) * (1/10) = 1/2402400.
So, the probability is approximately 1 in 2,402,400. You'd think it's a rare occurrence, but hey, stranger things have happened at the racetrack!
To find the probability of 5 horses owned by one person finishing first, second, third, fourth, and fifth in a horse race with 14 entries, we first need to calculate the total number of possible outcomes or the total number of ways the race can finish.
The total number of outcomes or ways the race can finish is equal to the number of arrangements or permutations of the 14 horses, which is given by the formula:
P(n, r) = n! / (n - r)!
Where P(n, r) represents the number of permutations of n items taken r at a time, and n! represents the factorial of n.
In this case, we want to calculate P(14, 5) since we are selecting 5 horses out of 14 to finish in a specific order.
P(14, 5) = 14! / (14 - 5)! = 14! / 9!
Simplifying,
P(14, 5) = (14 x 13 x 12 x 11 x 10 x 9!) / 9!
The factorials in the numerator and denominator cancel out,
P(14, 5) = 14 x 13 x 12 x 11 x 10 = 240,240
So, there are 240,240 possible outcomes or ways the race can finish.
Now, to calculate the probability of the desired outcome, where 5 horses owned by one person finish first, second, third, fourth, and fifth, we need to consider that there is only 1 way this outcome can occur.
Therefore, the probability of this outcome is given by:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 240,240 = 0.000004163
So, the probability that 5 horses owned by one person finish first, second, third, fourth, and fifth in a horse race with 14 entries is approximately 0.000004163.
To find the probability of 5 horses owned by 1 person finishing in the top 5 positions, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes: In a horse race with 14 entries, the first position can be occupied by any of the 14 horses. Once the first position is filled, the second position can be occupied by any of the remaining 13 horses, and so on. Therefore, the total number of possible outcomes is:
14 * 13 * 12 * 11 * 10 = 240,240
Number of favorable outcomes: We want to find the number of ways in which 5 horses owned by 1 person can finish in the top 5 positions. Since all 5 horses must finish in the top 5, we can consider the number of ways in which they can occupy the first 5 positions. The first position can be filled by any of the 5 horses, the second position by any of the remaining 4, and so on. Therefore, the number of favorable outcomes is:
5 * 4 * 3 * 2 * 1 = 120
Now, we can calculate the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 120 / 240,240
≈ 0.000499
Therefore, the probability that 5 horses owned by 1 person finish first, second, third, fourth, and fifth in a horse race with 14 entries is approximately 0.000499.