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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

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

Grade:

2 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
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

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