In a competition, only the top 3 horses receive prizes. How many possible ways can a 1st, 2nd, and 3rd prize be awarded if the competition has 12 horses?
A. 36
B. 220
C. 440
D. 1320
Also, is this a permutation or a combination?
Please Help!!
Thank you.
It is a permutation, because the order in which they finish matters. The answer is 12*11*10 = (D)
To find the number of possible ways the prizes can be awarded, we need to use the concept of permutations. Since each prize can only be awarded to one horse, and the order matters (1st place, 2nd place, and 3rd place), we need to use the formula for permutations.
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 we are choosing at a time.
In this case, we have 12 horses and we need to choose 3 horses for the prizes.
Using the formula for permutations, we can calculate:
P(12, 3) = 12! / (12 - 3)!
= 12! / 9!
12! is equal to 12 x 11 x 10 x 9!, and 9! cancels out in the numerator and denominator.
P(12, 3) = 12 x 11 x 10
= 1,320
Therefore, there are 1,320 possible ways the 1st, 2nd, and 3rd prizes can be awarded to the horses.
The correct answer is D. 1,320.
And to answer your second question, since the order matters and each prize can only be awarded to one horse, this is a permutation.