At a round table, n persons are seated on n chairs. The probability that two friends from same college are sitting next to each other, is:
Step 1 — Total circular arrangements: Seating \(n\) distinct persons around a round table gives \((n-1)!\) arrangements.
Step 2 — Favourable arrangements: Treat the two friends as one block. The block plus the other \((n-2)\) persons gives \((n-2)!\) circular arrangements, and the two friends can be arranged within the block in \(2!\) ways. Favourable count \(=2\,(n-2)!\).
Step 3 — Probability:
\[P=\frac{2\,(n-2)!}{(n-1)!}=\frac{2}{n-1}\]
Hence the required probability is \(\dfrac{2}{n-1}\).
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