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January 13th, 2018, 08:51 AM  #1 
Member Joined: Dec 2017 From: Tel Aviv Posts: 54 Thanks: 3  Probablity  round table
How many ways there is when sitting next to round table of nchairs? How many ways there is if Dan and David don't want to sit together? What is the formula? 
January 13th, 2018, 11:47 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,791 Thanks: 923 
Sitting how many people? n?

January 13th, 2018, 12:39 PM  #3 
Member Joined: Dec 2017 From: Tel Aviv Posts: 54 Thanks: 3 
Yes, n people.

January 13th, 2018, 01:07 PM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 1,791 Thanks: 923  suppose the table was linear rather than circular. how many different ways could you arrange n people? now given that table is circular, how many of those arrangements are in fact identical for a given arrangement. given the two answers above what is the formula for the # of arrangements around an n seat circular table? 
January 13th, 2018, 04:03 PM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,865 Thanks: 768  
January 15th, 2018, 12:54 AM  #6  
Member Joined: Dec 2017 From: Tel Aviv Posts: 54 Thanks: 3  I don't know Quote:
And why n >= 4 (because of the round table (?!))?  
January 15th, 2018, 03:17 AM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,865 Thanks: 768 
If n = 3, then 3 chairs only: so they have to be next to each other, being a round table! 
January 15th, 2018, 03:35 AM  #8 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,767 Thanks: 1018 Math Focus: Elementary mathematics and beyond 
What about n = 1? 
January 15th, 2018, 04:08 AM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,865 Thanks: 768 
Easy: Dan and David kiss n' make up, Dan sits on David's lap 

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probablity, round, table 
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