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few more of P&C
by fundoo bond - Friday, 7 September 2007, 04:02 PM
  Three variants of CAT paper are to be given to 12 students. In how any ways can the students be placed in 2 rows of 6 each so that there should be no identical variants side by side and that the student sitting behind should get the same variant. Find the number of ways it can be done.

a) 6!^2 b) 6 x 6! x 6! c) 6!^3 d) 30 x (12 C 6) x 6! x 6!

i can figure out the ans is d).
no. of arranging students
(12 C 6) x 6! x 6!.

but i m not getting how no. of ways arranging the variants will be 30.
somebody help plz...

regards,
fundoo
Re: few more of P&C
by trosin .. - Friday, 7 September 2007, 06:43 PM
 

if its clear that no. of seatin arrangement is 12C6*6!*6! then now take three sets of papers as a,b,c .as student one behind the other are havin same paper so arrangement of first row will b same as of second row in terms of paper,so leave second row now ...for d 1st row...

a can be given to 2 students in 6C2 ways out of those 5 ways will b such dat they r together hence leavin 10 ways . Now out of 4 places 2 for b can be selected in 4c2 ways out of those 3 ways r wre they r together thus leavin 3 ways,thus total 30 ways...hence the answer.

one thing of caution this answer is wen we r distributing 4 papers each of a,b,c....if distribution of no. of copies is not restricted to 4 then paper distribution is...3*2*2*2*2*2=96

hey fundoo tel me if m goin rite...

Re: few more of P&C
by Sri KLR - Friday, 7 September 2007, 07:03 PM
 

@trosin,

I think it should be 3.2^5 only...i.e 96 thoughtful

I didn't get your solution..for getting 30

Re: few more of P&C
by trosin .. - Friday, 7 September 2007, 07:07 PM
  wat happened klr...if tre is ristriction of distribution 4 papers each of three variants den ans w'ld b 30...
Re: few more of P&C
by Sri KLR - Friday, 7 September 2007, 07:16 PM
 

take teh papers a,b,c

now let the persons in the first row be

X1,X2,X3,X4,X5,X6

Now the first paper( selected in 3 ways) can be given to first person. Second person can be given only from two papers...and even 3,4,5 and 6th persons can be given in only 2 ways...hence 3.2^5....ain't it?

Re: few more of P&C
by trosin .. - Friday, 7 September 2007, 07:26 PM
  this answer is includin the cases wen u r distributin 6 a,4 b and 2 c...and other....if each is to b distributed equally...then answer w'ld b 30...
Re: few more of P&C
by Navdeep Tuli - Thursday, 23 October 2014, 04:16 AM
  Trosin, shouldn't it be multiplied by 2 as well as there are 2 rows? this is for just one row?