P&C Yet Again!!

parallel_chase · Posted: Wed Aug 20, 2008 5:30 am Post subject: P&C Yet Again!!

Two variants of a test paper are distributed among 12 students. How many ways are there of seating the students in two rows so that students sitting side by side do not have identical papers and those sitting in the same column have the same paper ?

A) 2*(6!)*(6!)

B) (12C6)*2*(6!)*(6!)

Since there are only two options available, I am more interested in the method as compared to the answer.

sudhir3127 · Posted: Wed Aug 20, 2008 5:44 am Post subject: Re: P&C Yet Again!!

pepeprepa · Posted: Wed Aug 20, 2008 5:53 am Post subject:

We disagree on this one... I am for A)

Here is my logic:
We have two possibilities of organizing the students.
XYXYXY
XYXYXY
or
YXYXYX
YXYXYX

for the X we have 6! possible combinations and for the Y we have the same so 6!*6!

Given we have 2 possibilities: 2*6!*6!

parallel_chase · Posted: Wed Aug 20, 2008 6:55 am Post subject:

Thanks for your inputs.

The answer is B. I think the way Sudhir did is the right way but definitely not the fastest.

Pepeprepa I did exactly the way you did initially but A is incorrect.

I request Ian/Stuart kindly give some insights........

gabriel · Posted: Wed Aug 20, 2008 10:24 am Post subject:

pepeprepa · Posted: Wed Aug 20, 2008 10:40 am Post subject:

Thank you for this precision, I missed this point... indeed what bothered me is that I couldn't totally represent me the situation and I don't know why, I will do it again later.

nervesofsteel · Posted: Wed Aug 20, 2008 5:26 pm Post subject:

first select 6 students from 12 who needs to be seated in first column..
it can be done in 12C6 ways.. Now arrange them in 6! ways..

Now the remaining 6 students can be seated in 6! ways in second column

But each column can have first set or second set
so there are 2 ways papers can be distributed.

so answer is 2*12C6* 6!*6!