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 = 210C.Combination; number of ways = 35D.Permutation; number of ways = 210SUBMITarrow_backPREVIOUS
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 = 210C.Combination; number of ways = 35D.Permutation; number of ways = 210SUBMITarrow_backPREVIOUS
Solution
This is a permutation problem because the order in which the runners finish matters (first, second, and third place are different outcomes).
In a permutation problem, we use the formula nPr = n! / (n - r)!, where n is the total number of options, r is the number of options chosen at a time, and "!" denotes a factorial, which means multiplying all positive integers up to that number.
Here, we have 7 runners (n = 7) and we are choosing 3 of them to award medals (r = 3).
So, the number of ways to award the medals is 7P3 = 7! / (7 - 3)! = 765 = 210.
So, the answer is D. Permutation; number of ways = 210.
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