In how many ways can 14 people be seated around a rectangular table having 5 seats along the longer side and 2 seats along the shorter side?
I tried to solve this and thought of it as a circular table with 14 positions. And my answer was $\frac{13!}{2}$. But it came wrong.
Where I went wrong and how should I steer in the correct direction?
The first person has $7$ options (he is the one who determines the orientation/ break symmetry).
After that, the other can choose their seat.
Hence in total, there are $7 \cdot 13!$ ways.