Sets of Outcomes Help: How many different answer sheets are possible?

elirj97

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[FONT=&quot]My brain is not really working rn and I really need help. PLEEEASE[/FONT]
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[FONT=&quot]A multiple choice test has 10 questions, and there are 5 choices for the answer to each question. An answer sheet has 1 answer for each question. [/FONT]
[FONT=&quot]a) How many different answer sheets are possible?[/FONT]
[FONT=&quot]b) How many different answer sheets are possible if the same answer is not used for every question?[/FONT]
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[FONT=&quot]Consider the following experiment. A coin is tossed repeatedly, and the result (H or T) of each toss is recorded. The experiment stops if there are two consecutive tosses with the same result (ex. TT, THH) or if the coin is tossed three times (example: THT). How many possible outcomes are there for this experiment? [/FONT]
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[FONT=&quot]HELP MEEEE[/FONT]
 
My brain is not really working …
Maybe you just need to take a break for awhile? :cool:

Please read the forum guidelines. This is a tutoring web site. We would like to know what you already understand about these exercises. Show us any attempts that you've made (even if you think they're wrong). If you can explain why you're stuck or tell us what parts you don't understand or recognize, it will help the volunteer tutors here to determine where to begin helping you. Thanks!
 
My brain is not really working rn and I really need help. PLEEEASE
We'll be glad to help! But first, we need to know what sort of help you're needing. Can you not even get started, so you need links to online lessons, so you can learn the background information? Or you can get started, but you're getting stuck part of the way? Either way, we need to know (with a clear listing of your steps, if your case is the latter).

1. A multiple choice test has 10 questions, and there are 5 choices for the answer to each question. An answer sheet has 1 answer for each question.
a) How many different answer sheets are possible?
b) How many different answer sheets are possible if the same answer is not used for every question?
Are we to assume that the answer sheets contain only correct answers, or are we to assume that these sheets are usually a joke, containing wrong answers?

Consider the following experiment. A coin is tossed repeatedly, and the result (H or T) of each toss is recorded. The experiment stops if there are two consecutive tosses with the same result (ex. TT, THH) or if the coin is tossed three times (example: THT). How many possible outcomes are there for this experiment?
What have you considered, with respect to probabilities for the various cases?

Please be complete. Thank you! ;)
 
We'll be glad to help! But first, we need to know what sort of help you're needing. Can you not even get started, so you need links to online lessons, so you can learn the background information? Or you can get started, but you're getting stuck part of the way? Either way, we need to know (with a clear listing of your steps, if your case is the latter).


Are we to assume that the answer sheets contain only correct answers, or are we to assume that these sheets are usually a joke, containing wrong answers?


What have you considered, with respect to probabilities for the various cases?

Please be complete. Thank you! ;)

I am sorry but I am writing it textually from the book, I am not leaving out anything. There is no additional info anywhere in the book.
 
Maybe you just need to take a break for awhile? :cool:

Please read the forum guidelines. This is a tutoring web site. We would like to know what you already understand about these exercises. Show us any attempts that you've made (even if you think they're wrong). If you can explain why you're stuck or tell us what parts you don't understand or recognize, it will help the volunteer tutors here to determine where to begin helping you. Thanks!

I don't understand anything and I have tried doing trees plus using the multiplication principle. I sort of came up with an answer for 1 a and 2, but not for 1 b.
 
… I have tried doing trees plus using the multiplication principle. I sort of came up with an answer for 1 a and 2, but not for 1 b.
Good. We'd like to see what you've tried. Can you describe your steps, doing trees? How did you apply the multiplication principle? Please share your answers for 1a and 2, even if you think they're wrong.
 
1. A multiple choice test has 10 questions, and there are 5 choices for the answer to each question. An answer sheet has 1 answer for each question.
a) How many different answer sheets are possible?
b) How many different answer sheets are possible if the same answer is not used for every question?

I am writing it textually from the book, I am not leaving out anything.
Well, then we'll have to use what we know from "real life". There being only one valid answer to each question (how else could the test be graded?) and answer sheets being a listing of the correct answers, there can be only one answer sheet.

However, that leaves us with part (b), which makes no sense under the above assumptions. If the answer sheets are allowed to list the letters for multiple-choice options which are not the correct answer (because "the same answer is not used for every question" for these sheets), then I guess you need to compute how many permutations of options can be listed. For question 1 on the test, there are five options, only one of which is correct. But the answer sheet is allowed to list any of the options, including the four incorrect options. So how many possibilities are there for question 1? And so forth.

What a strange exercise.... :shock:
 
Well, then we'll have to use what we know from "real life". There being only one valid answer to each question (how else could the test be graded?) and answer sheets being a listing of the correct answers, there can be only one answer sheet.

However, that leaves us with part (b), which makes no sense under the above assumptions. If the answer sheets are allowed to list the letters for multiple-choice options which are not the correct answer (because "the same answer is not used for every question" for these sheets), then I guess you need to compute how many permutations of options can be listed. For question 1 on the test, there are five options, only one of which is correct. But the answer sheet is allowed to list any of the options, including the four incorrect options. So how many possibilities are there for question 1? And so forth.

What a strange exercise.... :shock:

I think the problem is about POSSIBLE answer sheets, as if you made up the answers before making the test, so that correctness doesn't come into it. (That actually makes sense, as you might want to put the correct answer to each problem in the place you randomly chose beforehand, to avoid having an unintentional pattern.) Or, possibly, "answer sheet" means the answers a student turns in, and anything is possible. In any case, it's just about possibilities, not about correctness.

This could also come up later in a probability problem, asking the probability that a student would get a certain score by randomly filling in an answer for each question. Randomness is the key idea.
 
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