Combinatorics Question (1 Viewer)

[yiaghertop]

Four boys and five girls are to be seated around a circular table. A particular boy X does not want to sit next to any of the girls and a particular girl Y does not want to sit next to any of the boys. How many arrangements are possible?

The solution is

Spoiler: answer

1728

, if someone could please explain the logic, that would be great!!

 

[yiaghertop]

got it actually!

I made BXB one group and fixed it, so the options for the boys around X will be 3 x 2.

Then, I made GYG another group, so the options for the girls around Y will be 4 x 3.

So, the 3 others and the GYG group can be arranged in 4! ways.

Therefore, the answer is 3 x 2 x 4 x 3 x 4! = 1728

Hope this helps for anyone else who tried and didn't get it!