In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?

In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people? Correct Answer <sup>15</sup>C<sub>7</sub> × 6! × 7!

'n' objects can be arranged around a circle in (n - 1)! ways.If arranging these 'n' objects clockwise or counter clockwise means one and the same, then the number arrangements will be half that number.i.e., number of arrangements = $$\frac{{\left( {n - 1} \right)!}}{2}$$You can choose the 7 people to sit in the first table in 15C7 ways.After selecting 7 people for the table that can seat 7 people, they can be seated in:(7 - 1)! = 6!The remaining 8 people can be made to sit around the second circular table in:(8 - 1)! = 7! Ways.Hence, total number of ways: 15C7 × 6! × 7!
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