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At a competition with 6 runners, 2 medals are awarded for first and second place.Each medal is different. How many ways are there to award the medals?A.720B.15C.30D.36

Question

At a competition with 6 runners, 2 medals are awarded for first and second place.Each medal is different. How many ways are there to award the medals?A.720B.15C.30D.36

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Solution

This is a permutation problem. The number of ways to award the medals can be calculated using the formula for permutations:

P(n, r) = n! / (n - r)!

where n is the total number of runners (6), r is the number of medals (2), and "!" denotes factorial.

Step 1: Calculate n! = 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720

Step 2: Calculate (n - r)! = (6 - 2)! = 4! = 4 * 3 * 2 * 1 = 24

Step 3: Substitute these values into the formula to find the number of ways to award the medals:

P(6, 2) = 720 / 24 = 30

So, there are 30 ways to award the medals. The correct answer is C.30.

This problem has been solved

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