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:

Key Insight:

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.

Calculation:

• 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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