Hello, and thanks in advance.

Four adults and 4 children are to be seated around a circular table. A particular child cannot sit next to any adult and a particular adult cannot sit next to any child.

Find how many such arrangements are possible.

not sure i have done this correctly and was hoping for some guidance.

Let the child that cannot sit next to adult be C1 and the adult that cannot sit next to any child be A1

Seat C1 in position 1 leaving only positions 4, 5, 6 for A1 = 3!

Seat A1

this leaves 3! positions for the remaining children

and 2! for the remaining adults

Total = 3! x 3! x 2!

= 72 ways

would appreciate confirmation if this is correct number of ways (i have no solution set)

or if i am completely on the wrong track