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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.
please answer both of the questions.
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....
please explain it wouldn't it be 11! ?
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.....
@MrNood you are wrong this is a circular permutation...can't you see its a round table?
12 tables yes?
single round table
yeah how many chairs i meant
infinite isn't the issue here.
matters! what if there were less tables to seat on
there aren't brother its the governor!
hmm 12^12 is number of ways they can seat if we don't care about who seats where
nah...you are wrong on what base are you assuming that?
just my guts! but then i didn't include the governor himself
its 11! ways but need some confirmation and help....@xapproachesinfinity you are not good at permutation are you?
@ganeshie8 is good at this but he isn't online!
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?
according to the wolf: http://mathworld.wolfram.com/CircularPermutation.html 11! appears to be right if the governor is standing by himself....
I thought so but the answer provided at the end of my book contradict my theory!
@ganeshie8 !! need assistance asap!!
is it 12! then the governor is taking a seat too :)
no governor is a good guy he doesn't wants a seat he will just sit on the floor.
hahahaaa @Ehsan18 so wats the ans at ur book there?
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...
the wolf mentions that as "inequivalent when flipping the circle is allowed" n the eqn becomes P'n = (n-1)!/2
may be but should just memorize it without concept?
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
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!
@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.