To solve the problem of finding the number of distinct arrangements of 8 people around a circular table (where rotations are considered identical), we can use the principles of circular permutations:
For linear permutations of (n) distinct objects, there are (n!) ways. However, in circular arrangements, rotating the table does not create a new arrangement. Each unique circular arrangement corresponds to (n) linear arrangements (one for each rotation). Thus, we divide the total linear arrangements by (n) to account for rotational symmetry.
For (n=8):
Number of distinct circular arrangements = (\frac{8!}{8} = 7!)
Compute (7!):
(7! = 7×6×5×4×3×2×1 = 5040)
Answer: (\boxed{5040})
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