Does the problem involve permutations or combinations? Do not solve.

The matching section of an exam has 3 questions and 7 possible answers. In how many different ways can a student answer the 3 questions, if none of the answer choices can be repeated?

Question

Does the problem involve permutations or combinations? Do not solve.

The matching section of an exam has 3 questions and 7 possible answers.  In how many different ways can a student answer the 3 questions, if none of the answer choices can be repeated?

BlackTom AI · Accepted Answer

The prompt asks us to classify the problem as involving either permutations or combinations, without actually performing the calculation.
Option 1: combination. This would be the appropriate choice if the order of selecting answers mattered less and we were only concerned with which subset of answers is used, not which question gets which answer. However, in this scenario, the 3 questions on the exam are distinct, so assigning which answer goes to which question matters. A combination would ignore the assignment to specific questions, which would undercount possibilities.
Option 2: permutation. This is the correct conceptual fit because each of the 3 questions is distinct, and we cannot repeat answers. The sequence in which we assign 3 distinct answers from 7 to the 3 questions matters: question A could receive answer X, B could receive Y, C could receive Z, and swapping Y and Z would produce a different overall arrangement. This aligns with the idea of ordered arrangements where no repetition is allowed.
In contrast, the core misconception behind choosing combination would be treating the problem as if the order of assigning answers to questions is irrelevant, which is not the case here since each question is different and the specific mapping of answers to questions constitutes a separate outcome.
So the correct framework is permutation, because we are counting ordered selections without repetition from 7 options for 3 distinct positions (the 3 questions).

Does the problem involve permutations or combinations? Do not solve. The matching section of an exam has 3 questions and 7 possible answers. In how many different ways can a student answer the 3 questions, if none of the answer choices can be repeated?单项选择题

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