Ehsan18
  • Ehsan18
The governor pf Punjab calls a meeting of 12 officers. In how many ways can they be seated at a round table?
Mathematics
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Ehsan18
  • Ehsan18
The governor pf Punjab calls a meeting of 12 officers. In how many ways can they be seated at a round table?
Mathematics
schrodinger
  • schrodinger
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Ehsan18
  • Ehsan18
Ehsan18
  • Ehsan18
Find the number of ways in which 5 men and 5 women can be seated at a round table in such a way that no two persons of the same sex sit together.
Ehsan18
  • Ehsan18
please answer both of the questions.

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MrNood
  • MrNood
how about YOU answer the questions? for the first one: there are 12 people - choose a seat - how many ways can that be filled ? ans = 12 now there are 11 people so the next seat - how many ways can THAT be filled? so there are 12 * 11 ways the first 2 seats can be filled Use your reasoning to work out how many way 12 seats can be filled....
Ehsan18
  • Ehsan18
please explain it wouldn't it be 11! ?
MrNood
  • MrNood
the first person to sit has 12 choices the second has 11 choices (so there is 12 * 11 possible options for those 2) the 3rd person has 10 choices (so there are 12* 11*10 ways that 3 can sit) continue this logic for all 12 people.....
Ehsan18
  • Ehsan18
@MrNood you are wrong this is a circular permutation...can't you see its a round table?
Ehsan18
  • Ehsan18
xapproachesinfinity
  • xapproachesinfinity
12 tables yes?
Ehsan18
  • Ehsan18
single round table
xapproachesinfinity
  • xapproachesinfinity
yeah how many chairs i meant
Ehsan18
  • Ehsan18
infinite isn't the issue here.
xapproachesinfinity
  • xapproachesinfinity
matters! what if there were less tables to seat on
Ehsan18
  • Ehsan18
there aren't brother its the governor!
xapproachesinfinity
  • xapproachesinfinity
hmm 12^12 is number of ways they can seat if we don't care about who seats where
Ehsan18
  • Ehsan18
nah...you are wrong on what base are you assuming that?
xapproachesinfinity
  • xapproachesinfinity
just my guts! but then i didn't include the governor himself
Ehsan18
  • Ehsan18
its 11! ways but need some confirmation and help....@xapproachesinfinity you are not good at permutation are you?
Ehsan18
  • Ehsan18
@ganeshie8 is good at this but he isn't online!
xapproachesinfinity
  • xapproachesinfinity
it is not 11! i guarantee you that say you have n people and we need k of them but we don't care how they will seat in how many way can they seat?
sdfgsdfgs
  • sdfgsdfgs
according to the wolf: http://mathworld.wolfram.com/CircularPermutation.html 11! appears to be right if the governor is standing by himself....
Ehsan18
  • Ehsan18
I thought so but the answer provided at the end of my book contradict my theory!
Ehsan18
  • Ehsan18
@ganeshie8 !! need assistance asap!!
sdfgsdfgs
  • sdfgsdfgs
is it 12! then the governor is taking a seat too :)
Ehsan18
  • Ehsan18
no governor is a good guy he doesn't wants a seat he will just sit on the floor.
sdfgsdfgs
  • sdfgsdfgs
hahahaaa @Ehsan18 so wats the ans at ur book there?
Ehsan18
  • Ehsan18
19958400
sdfgsdfgs
  • sdfgsdfgs
ahhhh it is the clockwise vs counter-clockwise thing..... 11!/2 = 19958400 it is half because clockwise n counter-clockwise count as the same; even though it is not specified in ur prob there...
sdfgsdfgs
  • sdfgsdfgs
the wolf mentions that as "inequivalent when flipping the circle is allowed" n the eqn becomes P'n = (n-1)!/2
Ehsan18
  • Ehsan18
may be but should just memorize it without concept?
sdfgsdfgs
  • sdfgsdfgs
the concept is fine but ur prob is not specific as to whether CW n CCW count as 1 or 2...it should have said something on that if its expecting u to give that ans
Ehsan18
  • Ehsan18
its probably because the governor is sitting on the floor so the table will be upside down and in upright positions both so there's how I will keep my concept steadfast!
sdfgsdfgs
  • sdfgsdfgs
@Ehsan18 i dont think dats wat ur teach has in mind when he wrote the prob! lol but whatever works for u is good :) the prob is not very clearly defined.

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