Anonamy wrote:
How do we arrive at 6!/6? I had chosen the answer for 6! only. What is the logic behind this please?
Hi,
in a normal row, say abcdef is the number of chair and mr x is one of the person sitting on these chairs...
in normal scenario/row , the moment x sits on a different chair a,b,c,d,e, or f, it is a new arrangement...
but it is different in case of a circle.. the seating arrangement is continous, there is no edge..
so say 1,2,3,4,5,6 are sitting on a,b,c,d,e,f respectively...
when they shift a sit to the right, the sitting arrangement becomes 6,1,2,3,4,5, which is different from 1,2,3,4,5,6( total 6 such arrangements)...
but in a circle 1,2,3,4,5,6 is same as 6,1,2,3,4,5 is same as 5,6,1,2,3,4.. because you are getting the same arrangement of people even if they have changed their seat because the relative positions have not changed.. that is why we divide by 6
Hope , the logic is clear
Thank you for explaining the logic behind 6!/6.
I am not the type of person who can just "memorize" a formula without understanding the logic behind it.
Hope the GMATClub community can benefit from my takeaway.
I got the wrong answer today, because I used the 6! formula which turns out to be the wrong logic as per your explanation.
Should similar question appears on the exam, I must get this type of question right.
Action item for exam: in a time-pressured situation, BE VERY CLEAR what the question is asking you for. Does it make sense for 6! ? Are you sure you are not double-counting any arrangement ? Draw it out (especially when you are not sure about which formula to use).