Question

6 persons sit around a table. In how many ways can they sit so that no person has the same neighbors?

Answer 1

By "neighbors," you mean ? Not quite sure of that aspect of the question.

Answer 2

if a is sitted beside b and c, then on the other permutation, they could no longer be with each other...

Answer 3

"The number of ways of arranging n persons along a round table so that no person has the same two neighbours is (n-1)!/2

courtesy of @candid @m8 at the following link:

http://tinyurl.com/d5c22g9

Answer 4

why divide by 2?

Answer 5

Great study page for circular permutations: http://www.ilovemaths.com/3permcirc.asp

Answer 6

If the link does not go directly to the permutations page, go to
http://www.ilovemaths.com and follow this sequence of clicks:

Classroom --> Classes --> Classes 11,12 --> Permutations/Combinations --> Circular Permutations