In how many ways can 4 dogs and 4 cats be seated at a circular table if each dog sits directly between two cats? (Two seatings are considered the same if one can be rotated to form the other. All dogs and cats are distinguishable.)
Any help would be greatly appreciated :D
There are 4!*4! = 576 ways of arranging the cats and dogs.
I think that's incorrect because of the restriction about the dogs needing to sit between two cats.
The arrangement around the table must be of the form DCDCDCDC, where D stands for dog and C stands for cat. We can place the first dog anywhere; we then have 3! = 6 ways of placing the remaining dogs and 4! = 24 ways of placing the cats. This gives a total of 3! * 4! = 144 arrangements.