Nobody around me knows how to calculate it

[smiley1409]

Hello there,
at first I would like to tell that it´s quite hard for me to write this in English but I have no other choice. I got this example from my math teacher because she accused me and my friends of cheating during the test. Everyone got own math problem which we have to solve - then she will delete the bad mark. I would ask in some math forum in my country but I´m afraid she could see it. She made up these math problems specially for us - so there are no similar math problems on the Internet. She would know that it is from me. ? I spend a lot of time trying to calculate it but I´m completely lost.
The example: There is 20 math problems and in every (of those 20) math problems you can make 3 mistakes and count it in wrong (different) way. There are 3 girls and the girls "accidentally" (they cheated ?) made the same 6 mistakes in those 20 math problems. What is the probability?

So that's it. I hope someone here could help me. I don't even know if I should count it like - 60 possible mistakes, from this I choose 6 mistakes.. So 60nCr6? I don't think so.. And what with those 3 girls? Where to multiply it?
If you can count it for me, please tell me even the process how you get there. I would really like to understand it.
Thank you! ?

 

[JeffM]

There are two problems here.

First, it is not entirely clear what you are asking. Your English is decent but far from perfect.

Second, do you not see that if we give you the answer, you are cheating. You were given this problem to do on your own to prove that you did not cheat. If you do not do it on your own, what does that mean.

 

[Otis]

… There is 20 math problems and in every (of those 20) math problems you can make 3 mistakes and count it in wrong (different) way.

Hi smiley. Does this mean that each question is multiple-choice, listing four possible answers? In other words, for each question, there are three ways to select the wrong answer.

There are 3 girls and [they make] the same 6 mistakes in … 20 math problems. What is the probability?

Does this mean that each student missed the same six questions, and, for each of the six questions, they all picked the same wrong answer?

?

 

[Steven G]

I have a better question. Based on this post what is the probability that the student did cheat on the original test?

 

[smiley1409]

There are two problems here.

First, it is not entirely clear what you are asking. Your English is decent but far from perfect.

Second, do you not see that if we give you the answer, you are cheating. You were given this problem to do on your own to prove that you did not cheat. If you do not do it on your own, what does that mean.

Hah, thank you. ? I know. I'm working on my English but yeah - a lot of work in front of me.
I am asking what is the probability this could happen - 3 girls make the same 6 mistakes in 20 math problems (in every one of those 20 you can do 3 mistakes and count it in a wrong way).
And as for the second problem - you might have a point but let's consider this: I spent really really long time trying to solve this on my own. Then I asked my father, then a few of my classmates. They didn't know because this math problem is much harder than problems we usually solve at Math class. And my opinion it's better to try it (and trust me - I made a genuine effort) and then ask someone who can explain it and I will understand than leave it. I think my teacher knows really good that no one of us can solve things like this. She invented this on purpose - she probably wanted us to sit and think about it. And that's what I did.
So if you know how to count it, it would be nice if you helped me. You don't have to solve the whole problem but I just need a "kick" - at least to know where to start. I really don't want to copy what these people write there without understanding it.
Thank you.

 

[smiley1409]

Hi smiley. Does this mean that each question is multiple-choice, listing four possible answers? In other words, for each question, there are three ways to select the wrong answer.


Does this mean that each student missed the same six questions, and, for each of the six questions, they all picked the same wrong answer?

?

Hi
I tried to translate exactly what the teacher told me. So yes, I understood it in the same way like you - in theory there are 4 options (3 bad and 1 good one - but I really don't know if I should consider only the wrong ones or if I have to count with all 4 options). But my teacher asks what is the probability that all the girls make in their tests the same 6 mistakes.. So I should consider only the wrong ones, am I right? ?

Yes exactly! I meant it like that.


So Otis, if you can help me with solving (at least a bit), I will be really grateful. ?
Thank you!

 

[smiley1409]

I have a better question. Based on this post what is the probability that the student did cheat on the original test?

Hi Jomo,
I think that it is not that important in this case. Who never cheated at school?
Now I need a help with solving, not giving a lesson, which I have already got. ?