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 January 13th, 2018, 08:51 AM #1 Banned Camp   Joined: Dec 2017 From: Tel Aviv Posts: 87 Thanks: 3 Probablity - round table How many ways there is when sitting next to round table of n-chairs? 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: 2,375 Thanks: 1276 Sitting how many people? n?
 January 13th, 2018, 12:39 PM #3 Banned Camp   Joined: Dec 2017 From: Tel Aviv Posts: 87 Thanks: 3 Yes, n people.
January 13th, 2018, 01:07 PM   #4
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Quote:
 Originally Posted by policer Yes, n people.
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
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Quote:
 Originally Posted by policer How many ways there is if Dan and David don't want to sit together?
No way if n < 4

January 15th, 2018, 12:54 AM   #6
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I don't know

Quote:
 Originally Posted by romsek 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?
I have no idea how to solve this question? Please give me more hints.
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: 14,128 Thanks: 1003 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: 7,923 Thanks: 1123 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: 14,128 Thanks: 1003 Easy: Dan and David kiss n' make up, Dan sits on David's lap

 Tags probablity, round, table

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