The governor pf Punjab calls a meeting of 12 officers. In how many ways can they be seated at a round table?

- Ehsan18

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- Ehsan18

@ganeshie8 @Michele_Laino

- 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

please answer both of the questions.

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## More answers

- 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

please explain it wouldn't it be 11! ?

- 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

@MrNood you are wrong this is a circular permutation...can't you see its a round table?

- Ehsan18

@FlamePlaysMC

- xapproachesinfinity

12 tables yes?

- Ehsan18

single round table

- xapproachesinfinity

yeah how many chairs i meant

- Ehsan18

infinite isn't the issue here.

- xapproachesinfinity

matters! what if there were less tables to seat on

- Ehsan18

there aren't brother its the governor!

- xapproachesinfinity

hmm
12^12 is number of ways they can seat if we don't care about who seats where

- Ehsan18

nah...you are wrong on what base are you assuming that?

- xapproachesinfinity

just my guts! but then i didn't include the governor himself

- Ehsan18

its 11! ways but need some confirmation and help....@xapproachesinfinity you are not good at permutation are you?

- Ehsan18

@ganeshie8 is good at this but he isn't online!

- 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

according to the wolf:
http://mathworld.wolfram.com/CircularPermutation.html
11! appears to be right if the governor is standing by himself....

- Ehsan18

I thought so but the answer provided at the end of my book contradict my theory!

- Ehsan18

@ganeshie8 !! need assistance asap!!

- sdfgsdfgs

is it 12! then the governor is taking a seat too :)

- Ehsan18

no governor is a good guy he doesn't wants a seat he will just sit on the floor.

- sdfgsdfgs

hahahaaa @Ehsan18 so wats the ans at ur book there?

- Ehsan18

19958400

- 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

the wolf mentions that as "inequivalent when flipping the circle is allowed" n the eqn becomes
P'n = (n-1)!/2

- Ehsan18

may be but should just memorize it without concept?

- 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

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

@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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