Twenty guests plus the host (21 people total) are to be seated at a single round table. How many distinct circular seatings are possible (rotations considered identical)?

Introduction / Context:For n distinct people around one round table, rotations are considered identical, so the number of seatings is (n−1)!.

Given Data / Assumptions:

• Total people n = 21 (20 guests + 1 host).
• One round table; reflections considered distinct unless stated otherwise (standard convention).

Concept / Approach:Fix one person's seat to break rotational symmetry; arrange the remaining n−1 people linearly.

Step-by-Step Solution:Seatings = (21−1)! = 20!.

Verification / Alternative check:If reflections were also identified (rare for seating), dihedral reduction would apply; but typical seating problems use pure circular equivalence.

Why Other Options Are Wrong:19! and 18! correspond to incorrectly subtracting more symmetries; “Couldn’t be determined” is incorrect given the standard model.

Common Pitfalls:Confusing bracelets (with flips) and round seating (orientation matters, flips distinct).

Final Answer:20!