4. (10 points) A, B, C, D, and E are sitting around a circular table playing poker, with A having a fixed seat. If B and D cannot sit next to each other, then there are ( ) different ways to arrange the seating.
A. 10
B. 8
C. 12
D. 16
【Analysis】This problem is essentially arranging 4 people, Yi, Bing, Ding, and Wu, in a certain order. Therefore:
(1) The number of ways to arrange all 4 people is: $\mathbf{A}_{4}^{4}=24$.
(2) When Yi and Ding are adjacent, the arrangement can be divided into two steps: The first step is to treat the 2 people as 1 unit, the number of ways to do this is $\mathrm{A}_{2}^{2}=2$; The second step is to treat the bundled 2 people as 1 unit, and then arrange them with Bing and Wu, the number of ways to do this is $\mathrm{A}_{3}^{3}=6$. Therefore,

The number of ways for Yi and Ding to be adjacent is $2 \times 6=12$.
(3) The number of ways for all 4 people to be arranged - the number of ways for Yi and Ding to be adjacent = the number of ways for Yi and Ding to be non-adjacent.

Thus, the problem is solved.
【Solution】The number of ways to arrange Yi, Bing, Ding, and Wu is $\mathbb{A}_{4}^{4}=4 \times 3 \times 2 \times 1=24$.
The number of ways for Yi and Ding to be adjacent is $\mathrm{A}_{2}^{2} \times \mathrm{A}_{3}^{3}=2 \times 1 \times 3 \times 2 \times 1=12$.
The number of ways for Yi and Ding to be non-adjacent is $24-12=12$.
Therefore, the answer is: $C$.