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# The number of ways in which 7 persons can sit around a table so that all shall not have the same neighbours in any two arrangements is A. 360 B. 720 C. 270 D. 180

Saurabh Koranglekar
one year ago
Dear student

The answer is option a ….............6!/2

Regards
Vikas TU
14149 Points
one year ago

Since each person has 2 neighbors at a time, and there're 6 people other than him, there are 3 arrangements at most.(otherwise colliding arrangements must exist)

now let's find out a possible tuple of arrangements, by selecting along the circle, skipping 0,1 and 2 people each step.

note that an equivalent condition is that each one of the nCr(7,2)=21 possible pair of neighbors exist at most once in all arrangements (in this case exactly once).

here they are:

1–2–3–4–5–6–7–-1

1–3–5–7–2–4–6–-1

1–4–7–3–6–2–5–-1