Imagine there are $5$ people around a round table: A, B, C, D and E. A and D must sit together. C and E must not sit together. How many different ways can they be seated?
I know that with A and D sitting next to each other there are $12$ different arrangements; $(5-1)! - ((4-1)! \times 2) = 12$. Due to treating A and D as one unit. How do I include C and E not sitting next to each other into the equation?