At a competition with 7 runners, medals are awarded for first, second, and third places. Each of the 3 medals is different. How many ways are there to award the medals?Decide if this is a permutation or a combination, and find the number of ways to award the medals.A.Permutation; number of ways = 35B.Combination; number of ways = 35C.Combination; number of ways = 210D.Permutation; number of ways = 210
Question
At a competition with 7 runners, medals are awarded for first, second, and third places. Each of the 3 medals is different. How many ways are there to award the medals?Decide if this is a permutation or a combination, and find the number of ways to award the medals.A.Permutation; number of ways = 35B.Combination; number of ways = 35C.Combination; number of ways = 210D.Permutation; number of ways = 210
Solution
This is a permutation problem because the order in which the medals are awarded matters (i.e., getting a gold medal is different from getting a silver or bronze medal).
The formula for permutations is nPr = n! / (n - r)!, where n is the total number of items, r is the number of items to choose, and "!" denotes factorial.
In this case, n = 7 (the number of runners) and r = 3 (the number of medals to be awarded).
So, the number of ways to award the medals is 7P3 = 7! / (7 - 3)! = 765 = 210.
Therefore, the correct answer is D. Permutation; number of ways = 210.
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