(Solution) - At an upcoming family reunion five families each consisting -(2025 Original AI-Free Solution)

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At an upcoming family reunion, five families - each consisting of a husband, wife, and one child - are to be seated around a circular table. In how many ways can these 15 people be arranged around the table so that no family is seated all together? (Here, as in Example 8.9, two seating arrangements are considered the same if one is a rotation of the other.)