Georg has 8 children. Because Georg is a good father, he can distinguish each of his children. He also has 4 black hats and 4 gold hats. He puts the hats on his children's heads, and then puts his children in two circles (one on his left and one on his right) so that the colours of the hats of the children alternate around each of the two circles.

• It is possible to sit 2 children on the left and 6 children on the right.
• It is possible to sit 4 children on the left and 4 children on the right.
• It is possible to site 6 children on the left and 2 children on the right

Determine the number of ways in which Georg can arrange the children.