Question 1143763
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At given context, those two persons who are to sit next to each other, represent one object with 2 states.


So, the problem is about circular permutations of 7 objects, where one fixed object can be in one of the two states.


The number of circular permutations then is  {{{2*(7!/7)}}} = 2*6! = 2*6*5*4*3*2*1 = 1440.    <U>ANSWER</U>


The factor  "2"  accounts for the order AB or BA of the two selected persons sitting next to each other.
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On circular permutations, see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Persons-sitting-around-a-circular-table.lesson>Persons sitting around a cicular table</A> 

in this site.