manasdas Posted May 16, 2008 Share Posted May 16, 2008 1. In how many ways can five people sit around a circular table if one person can not have the same neighbors in any two arrangements? 2. Seven men and seven women have to sit around a circular table so that no 2 women are together. how many ways? Quote Link to comment Share on other sites More sharing options...
krovvidy Posted May 16, 2008 Share Posted May 16, 2008 1. In how many ways can five people sit around a circular table if one person can not have the same neighbors in any two arrangements? If there was no restriction 5 people can sit around a circular table in (5-1)! = 4! = 24 ways If you try to visualize this in a circle, you'll understand that out of these arrangements, half would be counter-clockwise equivalent to the other half ... Considering only one direction we have 24/2 = 12 ways. 2. Seven men and seven women have to sit around a circular table so that no 2 women are together. how many ways? Arranging 7 men around a circular table = 6! ways There would be 7 spots in between any two men in the above arrangments and the 7 women can sit in any of those 7 places in 7! ways (note: this is not a circular arrangement) So, the total ways = 6!*7! Quote Link to comment Share on other sites More sharing options...
mannu08 Posted May 17, 2008 Share Posted May 17, 2008 thanks for the explanation krovvidy :) Quote Link to comment Share on other sites More sharing options...
tarkumar Posted May 17, 2008 Share Posted May 17, 2008 1. 12 2. 6! * 7! Quote Link to comment Share on other sites More sharing options...
hi0parag Posted August 28, 2011 Share Posted August 28, 2011 If there was no restriction 5 people can sit around a circular table in (5-1)! = 4! = 24 ways If you try to visualize this in a circle, you'll understand that out of these arrangements, half would be counter-clockwise equivalent to the other half ... Considering only one direction we have 24/2 = 12 ways. Arranging 7 men around a circular table = 6! ways There would be 7 spots in between any two men in the above arrangments and the 7 women can sit in any of those 7 places in 7! ways (note: this is not a circular arrangement) So, the total ways = 6!*7! For Prob-1: how about the following circular arrangements: (In all four arrangements C has the same two neighbours - B & D) 1) ABCDE 2) EBCDA 3) EDCBA (Anti clockwise of 1) 4) ADCBE (Anti clockwise of 2) Shouldn't we be dividing (5-1)! by 4? For Prob-2: Why is the arrangement of women not considered circular? Quote Link to comment Share on other sites More sharing options...
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