Tough Permutations/Combinations problem

[Guest]

[Deleted because nobody provided a source for this question.]

I think the correct answer is A, but people claim the answer is B. Here's a diagram to explain my logic:

#1 #2 #1 #2 #1 #2
12 * 6 * 4 * 4 * 2 *2

5 * 5 *3 * 3 * 1 *1

Starting at the top left, any of the 12 students can sit in that seat. The person directly below him must have the same test, which means there are 5 students who could fill that spot. On to the second column, there are 6 students left who can receive the second test, then right below that choice, 5 (because the person in the same column, must get the same test). And so on...


if you split 12 into 6 *2, the answer comes out 6! * 6! *2... thus, the answer is A...

Can an expert explain why others are telling me the answer is B?

[Stockmoose16]

Can someone please answer this? I'd like the answer.

[RonPurewal]

the first thing you have to do is give the source of the problem, per the forum rules. we can't answer questions posted in this folder without attribution.
thank you.

also, the wording of this question leaves much to be desired:
* first of all, there's no guarantee that there are two equal rows of two students each. that is almost certainly the author's intention, but it's not specified in the wording of the problem, and one can easily construct legitimate situations with other numbers of students per row. those situations will create some "columns" of 1 student, but there's nothing prohibiting such "columns".
* also, the problem itself has sloppy wording. the question prompt is just "how many ways ... of seating the students", but it seems clear that we're looking for arrangements of students and papers.
* finally, the question is ambiguous on whether the test papers are handed to the students before they sit down (i.e., certain students are stuck with certain papers) or after they sit down (so that any student can get any paper). this definitely matters.

in any case:
* please post an attribution, or we'll take down the question;
* whatever source this question is from, run for your life! any source featuring questions with wording like this will not be helpful.

and finally, please give all five of the answer choices to any problem you post, even if you've ruled out the other three. thanks.

[shaji]

the first thing you have to do is give the source of the problem, per the forum rules. we can't answer questions posted in this folder without attribution.
thank you.

also, the wording of this question leaves much to be desired:
* first of all, there's no guarantee that there are two equal rows of two students each. that is almost certainly the author's intention, but it's not specified in the wording of the problem, and one can easily construct legitimate situations with other numbers of students per row. those situations will create some "columns" of 1 student, but there's nothing prohibiting such "columns".
* also, the problem itself has sloppy wording. the question prompt is just "how many ways ... of seating the students", but it seems clear that we're looking for arrangements of students and papers.
* finally, the question is ambiguous on whether the test papers are handed to the students before they sit down (i.e., certain students are stuck with certain papers) or after they sit down (so that any student can get any paper). this definitely matters.

in any case:
* please post an attribution, or we'll take down the question;
* whatever source this question is from, run for your life! any source featuring questions with wording like this will not be helpful.

and finally, please give all five of the answer choices to any problem you post, even if you've ruled out the other three. thanks.

"and finally, please give all five of the answer choices to any problem you post, even if you've ruled out the other three. thanks"
Indeed!!!.The other three choices may throw some light to aid comprehend the mind of the question setter. The beauty of this problem is to elliminate the impossible and choose the improbable however impossible it might seem as the correct answer!!!

[StaceyKoprince]

This question was deleted because no source was cited. Please read (and follow!) the forum guidelines before posting. We cannot reply unless a source is cited (and, if no source is cited, we will have to delete the post!). Thanks.