A student is asked to answer 7 out of 9 questions on an exam.
(a) Classify the problem as a permutation, a combination, or neither.
I'd say combination. The order in which the questions are answered does not matter.
To determine whether the problem is a permutation, a combination, or neither, we need to understand the difference between these two concepts.
Permutation: A permutation is an arrangement of objects in a specific order.
Combination: A combination is a selection of objects without considering the order.
In this case, the problem can be classified as a combination. Let me explain why:
The student is asked to answer 7 out of 9 questions on the exam. The order in which the questions are answered does not matter, as long as 7 out of the 9 questions are chosen.
If the problem were a permutation, the order in which the questions are answered would matter. For example, if the student had to answer the questions in a specific order, such as question 1, followed by question 2, and so on, it would be a permutation problem.
But since the problem only requires the student to choose 7 out of the available 9 questions, without considering the order in which they are chosen, it can be classified as a combination problem.