Questions: Is the selection below a permutation, a combination, or neither? Explain your reasoning. A father orders ice cream (chocolate, vanilla, or peach) for each of his 5 children. Choose the correct answer below. A. As a child getting vanilla is different from the same child getting peach, the order in the selection process is vital. Also, two children can both request the same type of ice cream. So, there are no repetitions in the selection process. Therefore, the selection is a permutation. B. As a child getting vanilla is different from the same child getting peach, the order in the selection process is irrelevant. Also, two children can both request the same type of ice cream. So, there will be repetition in the selection process. Therefore, the selection is neither a combination nor a permutation. C. As a child getting 4 nilla is different from the same child getting peach, the order in the selection process is irrelevant. Also, two children can both request the same type of ice cream. So, there are no repetitions in the selection process. Therefore, the selection is a combination. D. As a child getting vanilla is different from the same child getting peach, the order in the selection process is irrelevant. Also, two children can both request the same type of ice cream. So, there are repetitions in the selection process. Therefore, the selection is a permutation.

Is the selection below a permutation, a combination, or neither? Explain your reasoning. A father orders ice cream (chocolate, vanilla, or peach) for each of his 5 children. Choose the correct answer below. A. As a child getting vanilla is different from the same child getting peach, the order in the selection process is vital. Also, two children can both request the same type of ice cream. So, there are no repetitions in the selection process. Therefore, the selection is a permutation. B. As a child getting vanilla is different from the same child getting peach, the order in the selection process is irrelevant. Also, two children can both request the same type of ice cream. So, there will be repetition in the selection process. Therefore, the selection is neither a combination nor a permutation. C. As a child getting 4 nilla is different from the same child getting peach, the order in the selection process is irrelevant. Also, two children can both request the same type of ice cream. So, there are no repetitions in the selection process. Therefore, the selection is a combination. D. As a child getting vanilla is different from the same child getting peach, the order in the selection process is irrelevant. Also, two children can both request the same type of ice cream. So, there are repetitions in the selection process. Therefore, the selection is a permutation.
Transcript text: Is the selection below a permutation, a combination, or neither? Explain your reasoning. A father orders ice cream (chocolate, vanilla, or peach) for each of his 5 children. Choose the correct answer below. A. As a child getting vanilla is different from the same child getting peach, the order in the selection process is vital. Also, two children can both request the same type of ice cream. So, there are no repetitions in the selection process. Therefore, the selection is a permutation. B. As a child getting vanilla is different from the same child getting peach, the order in the selection process is irrelevant. Also, two children can both request the same type of ice cream. So, there will be repetition in the selection process. Therefore, the selection is neither a combination nor a permutation. C. As a child getting 4 nilla is different from the same child getting peach, the order in the selection process is irrelevant. Also, two children can both request the same type of ice cream. So, there are no repetitions in the selection process. Therefore, the selection is a combination. D. As a child getting vanilla is different from the same child getting peach, the order in the selection process is irrelevant. Also, two children can both request the same type of ice cream. So, there are repetitions in the selection process. Therefore, the selection is a permutation.
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Solution

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Solution Steps

To determine whether the selection is a permutation, combination, or neither, we need to consider two factors: whether the order of selection matters and whether repetition is allowed. In this scenario, each child can choose from three flavors, and the order in which they choose matters because each child is distinct. Additionally, repetition is allowed since multiple children can choose the same flavor. Therefore, this scenario is best described as a permutation with repetition.

Step 1: Determine the Nature of the Selection

In this problem, we need to determine whether the selection process is a permutation, combination, or neither. The key factors to consider are whether the order of selection matters and whether repetition is allowed. Here, each child can choose from three flavors of ice cream, and the order matters because each child is distinct. Additionally, repetition is allowed since multiple children can choose the same flavor.

Step 2: Calculate the Total Number of Ways

Since the order matters and repetition is allowed, we use the formula for permutations with repetition. The formula is given by:

\[ \text{Total Ways} = n^r \]

where \( n \) is the number of choices (flavors) and \( r \) is the number of selections (children). Substituting the given values:

\[ \text{Total Ways} = 3^5 = 243 \]

Final Answer

B. As a child getting vanilla is different from the same child getting peach, the order in the selection process is irrelevant. Also, two children can both request the same type of ice cream. So, there will be repetition in the selection process. Therefore, the selection is neither a combination nor a permutation.

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