At a competition with 5 runners, 5 medals are awarded for first place through fifth place. Each medal is different. How many ways are there to award the medals?Decide if the situation involves a permutation or a combination, and then find the number of ways to award the medals.A.Permutation; number of ways = 1B.Permutation; number of ways = 120C.Combination; number of ways = 120D.Combination; number of ways = 1
Question
At a competition with 5 runners, 5 medals are awarded for first place through fifth place. Each medal is different. How many ways are there to award the medals?Decide if the situation involves a permutation or a combination, and then find the number of ways to award the medals.A.Permutation; number of ways = 1B.Permutation; number of ways = 120C.Combination; number of ways = 120D.Combination; number of ways = 1
Solution
This situation involves a permutation because the order in which the medals are awarded matters (i.e., getting the first-place medal is different from getting the second-place medal).
To find the number of ways to award the medals, we use the formula for permutations of n items taken r at a time, which is nPr = n! / (n - r)!. In this case, there are 5 runners and 5 medals, so n = r = 5.
Therefore, the number of ways to award the medals is 5P5 = 5! / (5 - 5)! = 5! / 0! = 120.
So, the answer is B. Permutation; number of ways = 120.
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