At a competition with 6 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. Combination; number of ways =120 B. Combination; number of ways =20 C. Permutation; number of ways =20 D. Permutation; number of way: =120

At a competition with 6 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. Combination; number of ways =120 B. Combination; number of ways =20 C. Permutation; number of ways =20 D. Permutation; number of way: =120

Permutation; number of ways = 120.

Explanation

This is a permutation problem because the order in which the medals are awarded matters. To find the number of ways to award the medals, we use the formula for permutations: P(6,3) = 6! / (6-3)! = 6! / 3! = 6 x 5 x 4 = 120.

Related

Researchers investigated the possible beneficial effect on heart health of drinking black tea and whether adding milk to tea reduces any possible benefit. Twenty-four volunteers were randomly assigned to one of three groups. Every day for a month, participants in group 1 drank two cups of hot black tea without milk, participants in group 2 drank two cups of hot black tea with milk, and participants in group 3 drank two cups of hot water but no tea. At the end of the month, the researchers measured the change in each of the participants’ heart health.