Six delegates sit down at a round table with six equally spaced seats. Two of them, Ravi and Sneha, must be seated directly across the table from each other. Counting two seatings as the same when one is a rotation of the other, in how many ways can the six be seated?

Rotations count as one seating, so fix Ravi in a seat and use him as the reference point. The seat directly across the table from him is then one definite seat, and Sneha must take it — exactly 1 way, with nothing to swap. The remaining 4 delegates fill the other 4 seats in 4! = 24 ways. Trap $120=(6-1)$! is the unrestricted round-table count. Trap 48 answers a different condition, 'the two must sit next to each other': gluing them into one unit gives (5 − 1)! × 2! = $24\times 2=48$. Trap 720 = 6! is the straight-row count and forgets that turning the whole table gives the same seating.