In how many different ways can 7 people sit around 2 round tables , one of which has 3 and the other has 4 seats?
The answer to the question is 460
2026-04-06 19:33:10.1775503990
In how many different ways can 7 people sit around 2 round tables , one of which has 3 and the other has 4 seats?
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Pick which three people go to the smaller table. Let the youngest person sit down first wherever they like, it matters not where. Then clockwise from where that person chose fill in the remaining seats with the people who were chosen to go to the smaller table.
With the remaining four people do the same thing for the larger table.
$\binom{7}{3}\cdot 2!\cdot 3! = 420$