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
Please Help!!
Thank you.
Also, is this a permutation or a combination?
Please help!!
Thank you.
To solve this problem, we can use the concept of permutations. The number of ways to arrange the top 3 horses out of 12 is given by the formula:
P(n, r) = n! / (n - r)!
Where n is the total number of horses (12 in this case) and r is the number of horses being selected (3 in this case).
So, to find the number of possible ways, we can substitute n = 12 and r = 3 into the formula:
P(12, 3) = 12! / (12 - 3)!
= 12! / 9!
Simplifying further:
P(12, 3) = (12 * 11 * 10 * 9!) / 9!
= (12 * 11 * 10) / 1
= 1320
Therefore, the correct answer is D. 1320.