Ten horses are entered in a horse race. How many permutations of 1st, 2nd, and 3rd place winners are there?
10 different horses could come in first, that leaves 9 to come in second, and 8 to come in third,
so
what is 10x9x8 ??
To find the number of permutations for the 1st, 2nd, and 3rd place winners in a horse race with 10 horses, we can apply the concept of permutations.
A permutation is an arrangement of objects in a specific order. In this case, we need to find the number of permutations for the three winners.
To calculate the number of permutations, we can use the formula for permutations:
P(n, r) = n! / (n - r)!
Where n is the total number of objects (in this case, horses), and r is the number of objects we are arranging (in this case, the number of winners).
In this problem, we have n = 10 (horses) and r = 3 (winners).
Using the formula, we have:
P(10, 3) = 10! / (10 - 3)!
= 10! / 7!
= (10 * 9 * 8 * 7!) / 7!
= 10 * 9 * 8
= 720
Therefore, there are 720 different permutations of 1st, 2nd, and 3rd place winners in a horse race with 10 horses.