Question

7 sisters dine at a round table. They dine together till at least one of them dine with different neighbours i.e., they do not like to dine with same neighbours in any two arrangements. In a year how many days they dine together?

• A. 180
• B. 504
• C. 720
• D. 360

Answer 1

The correct option is D 360

Clearly 7 sisters can sit around a table in 6! ways. But in clockwise and anticlockwise arrangements each of the ladies have the same neighbours.
So, the required number of ways $=\frac{1}{2}\times (6!)=360$
Hence they dine together only 360 days.