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Eight people, including two specific people Anil and Bharti, are to…

Question

Eight people, including two specific people Anil and Bharti, are to be seated around a circular table with 8 seats. Two seatings are considered the same if one is a rotation of the other, but reflections are considered different. How many distinct seatings have Anil and Bharti NOT seated next to each other?

✓ Verified answer: 3600checked by our engine — not a guess

Step-by-step solution

Total circular seatings of 8 people (rotations identified, reflections distinct) = (8-1)! = 5040.

Count seatings where Anil and Bharti are adjacent: glue them into a block.

Treat the block plus the other 6 people as 7 'units' around the circle: (7-1)!

= 720 circular arrangements, and the block has 2 internal orders (Anil-Bharti or Bharti-Anil), giving 720*2 = 1440 adjacent seatings.

Non-adjacent = 5040 - 1440 = 3600.

Final answer3600

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