In a horse race, how many different finishes among the first 3 places are possible if 10 horses are running.
What is
10x9x8 = ???
720 its correct
To find the number of different finishes among the first 3 places in a horse race with 10 horses, we can use the concept of permutations.
In this scenario, we are selecting 3 horses out of 10 to determine the first, second, and third places. The order in which the horses finish matters, as each position represents a different outcome.
To calculate the number of different finishes, we can use the formula for permutations:
P(n, r) = n! / (n - r)!
Where "n" represents the total number of items, and "r" represents the number of items being selected.
In this case, we want to find P(10, 3), which is calculated as follows:
P(10, 3) = 10! / (10 - 3)!
= 10! / 7!
Calculating the factorial of each number:
P(10, 3) = (10 × 9 × 8 × 7!)/ 7!
= 10 × 9 × 8
= 720
Therefore, there are 720 different finishes among the first 3 places in the horse race.