SOLUTION: How many ways can 11 people be seated around a circular table if two of them insist to sit next to each other?

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Question 1180049: How many ways can 11 people be seated around a circular table if two of them insist to sit next to each other?

Answer by ikleyn(52776) About Me  (Show Source):
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How many ways can 11 people be seated around a circular table if two of them insist to sit next to each other?
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Then we consider this special pair as one (glued) object, and we, actually, 
have 10 objects then (instead of 11) to arrange around the circular table.



We can arrange 10 objects around the circular table by 9! ways,

but this special object can be in one of the two states (AB) or (BA).



Therefore, the total number of all possible arrangements (circular permutations) of this kind is


    2*9! = 2 * (9*8*7*6*5*4*3*2*1) =  725760.     ANSWER

Solved, answered and explained.