Question: Is the selection below a permutation, a combination, or neither? Explain your reasoning. A judge…

Is the selection below a permutation, a combination, or neither? Explain your reasoning. A judge awards 3 dogs first place, second place, and third place in a dog show. Choose the correct answer below. A. As the order that the dogs are chosen is important, the order in the selection process is irrelevant. Also a dog cannot win multiple places in the show, thus there are repetitions in the selection process. Therefore, the selection is neither a permutation nor a combination. B. As the order that the dogs are chosen is important, the order in the selection process is irrelevant. Also a dog cannot win multiple places in the show, thus there are no repetitions in the selection process. Therefore, the selection is a combination. C. As the order that the dogs are chosen is important, the order in the selection process is irrelevant. Also a dog cannot win multiple places in the show, thus there are no repetitions in the selection process. Therefore, the selection is a permutation. D. As the order that the dogs are chosen is important, the order in the selection process is vital. Also a dog cannot win multiple places in the show, thus there are no repetitions in the selection process. Therefore, the selection is a permutation.

Solution

To solve this problem, we need to determine if the selection of dogs is a permutation, combination, or neither. A permutation is used when the order of selection matters, while a combination is used when the order does not matter. In the given scenario, a judge awards 3 dogs first place, second place, and third place. Here, the order of selection is important because each dog gets a specific place (first, second, or third). Thus, the correct answer is C: As the order that the dogs are chosen is important, the order in the selection process is relevant. Also, a dog cannot win multiple places in the show, thus there are no repetitions in the selection process. Therefore, the selection is a permutation.