3 boy and 3 girls are to be seated around a table in a circle. Among them, the boy X does not want any girl neighbour and the girl Y does not want any boy neighbour. How many such arrangements are possible?

Explanation

Fix the positions of X and Y as shown in the figure.
Now, the boys `B_(1), B_(2)` and girls `G_(1),G_(2)` may have their neighbours X and Y respectively.
The boys `B_(1) and B_(2)` may be arranged among themselves in 2 ! ways. And, the girls `G_(1) and G_(2)` may be arranged among themselves in 2 ! ways.
Hence, the required number of arrangements `=(2xx2)=4.`