Solution
Alternating Delegations
Show the problem again
Five American diplomats and five British diplomats (all ten distinct people) sit at a round table with ten seats, so that nationalities alternate around the table. Seatings differing only by a rotation are the same; mirror images are different. How many seatings are possible? Give an integer.
Worked solution
The answer is 2880. Fix one American's seat to remove rotational symmetry. Alternation then forces the Americans into every other seat starting from hers, so the other four Americans fill their four seats in 4! = 24 ways and the five Britons fill the five seats between them in 5! = 120 ways. Total: 24 × 120 = 2880.
Source: Classic counting exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.