SOLUTION: On an English exam, students are required to answer four essay questions from a list of nine questions. How many different ways can they choose which four questions to answer?

Question 449485: On an English exam, students are required to answer four essay questions from a list of nine questions. How many different ways can they choose which four questions to answer?

I think that order does matter here, but I can't explain exactly why--so I am not sure. If it does matter, I would use a permutation, which would give me 3024. If it does not matter, I would use a combination, which would give me 126. But I feel like there are more than 126 ways. Any help you could give would be great!!
Thank you,
Nicole:)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Order doesn't matter at all here. Why? Consider labeling all the possible essays with numbers 1 through 9. Now let's say that a student makes the possible selections: 1, 3, 8, 9 (ie a student chose to answer questions 1, 3, 8, and 9).

Is this any different from 9, 3, 8, 1? Or how about 3, 9, 1, 8? No, these selections are the same 4 essays (the professor is probably going to sort them anyway). Unless the professor says "select 4 essays and choose which ones you want me to grade heaviest" (ie say a student is really confident about his/her first 2 choices 1 and 3, but not as confident in his/her second 2 choices 8 and 9, then s/he would say "put more weight towards choices 1 and 3"). Think of it as a curve of some sort, but only applied to that student's choices. But this is a bit elaborate and probably hardly used in academics. My guess is that each question has the same weight/importance as any other question.

So this gives us strong evidence to conclude that order does NOT matter, which means that a combination would be used. So the answer would be 126.
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