Eight different people, including Ravi and Tara, are to be seated around a round table. Two seatings are taken to be the same if one can be turned into the other just by everyone moving round the table together. In how many ways can they be seated if Ravi and Tara must always sit next to each other?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1440
\(n\) different units around a round table can be seated in \((n-1)!\) ways. People who must sit together are first tied into one block.
Block (Ravi + Tara) + 6 others = 7 units around the table: \((7-1)!=6!=720\) ways
Inside the block: Ravi-Tara or Tara-Ravi, \(2!=2\) ways
Ways \(=720\times2=1440\)
Why the other options are incorrect
Option (1) 720 — Incorrect. This is only \(6!\); it leaves out the 2 orders of Ravi and Tara.
Option (2) 5040 — Incorrect. This is \(7!\), all the round-table seatings of 8 people, with no condition.
Option (3) 10080 — Incorrect. This is \(7!\times2!\), which treats the 7 units as standing in a straight row instead of around a table.