there are 12 horses in a horse show competition. the top three winning horses receive money. how many possible money winning orders are there for a competition with 12 horses ?
1320
there are 12 horses in a horse show competition. the top three winning horses receive money. how many possible money winning orders are there for a competition with 12 horses ?
To calculate the number of possible money-winning orders for a competition with 12 horses, we can use the concept of permutations.
Since there are 12 horses competing, there are 12 options for the first-place horse. After the first-place horse is determined, there are 11 remaining options for the second-place horse. Finally, there are 10 options for the third-place horse.
The total number of possible money-winning orders can be calculated by multiplying these numbers:
12 options for first place × 11 options for second place × 10 options for third place
Therefore, there are a total of 12 × 11 × 10 = 1,320 possible money-winning orders for the competition with 12 horses.
To calculate the number of possible money winning orders for a competition with 12 horses, we can use the concept of permutations.
Since the top three winning horses are selected, we need to find the number of permutations of 12 horses taken 3 at a time. The formula for permutations is given by P(n, r) = n! / (n - r)!, where n is the total number of items and r is the number of items to be selected.
In this case, n = 12 (number of horses) and r = 3 (number of winning horses). Substituting these values into the formula:
P(12, 3) = 12! / (12 - 3)! = 12! / 9!
Now, let's simplify this expression:
12! = 12 × 11 × 10 × 9!
9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
By canceling out the common terms (9!) in the numerator and denominator:
P(12, 3) = (12 × 11 × 10) / (1) = 1320
Therefore, there are 1320 possible money winning orders for a competition with 12 horses.