4. (10 points) Arrange the numbers $1,2,3,4,5,6,7,8$ in a row so that the sums of the numbers on both sides of 8 are equal. How many different arrangements are there?
A. 1152
B. 864
C. 576
D. 288
【Analysis】First, find the sum of $1,2,3,4,5,6,7$ is 28, and determine that the sum of the numbers on both sides of 8 is 14; then divide into 4 cases: (1) when 8 is on one side with 1, 6, 7, and on the other side with 2, 3, 4, 5; (2) when 8 is on one side with 2, 5, 7, and on the other side with 1, 3, 4, 6; (3) when 8 is on one side with 3, 4, 7, and on the other side with 1, 2, 5, 6; (4) when 8 is on one side with 1, 2, 4, 7, and on the other side with 3, 5, 6; calculate the number of different arrangements in each case, and thus find the total number of different arrangements.

【Solution】Solution: $1+2+3+4+5+6+7=28$
The sum of the numbers on both sides of 8 is: $28 \div 2=14$
(1) When 8 is on one side with $1,6,7$, and on the other side with $2,3,4,5$,
the number of different arrangements is:
$$
\begin{aligned}
& (3 \times 2 \times 1) \times(4 \times 3 \times 2 \times 1) \times 2 \\
= & 6 \times 24 \times 2 \\
= & 288 \text { (ways) }
\end{aligned}
$$
(2) When 8 is on one side with $2,5,7$, and on the other side with 1, 3, 4, 6, the number of different arrangements is 288 ways.
(3) When 8 is on one side with 3, 4, 7, and on the other side with 1, 2, 5, 6, the number of different arrangements is 288 ways.
(4) When 8 is on one side with $1,2,4,7$, and on the other side with 3, 5, 6, the number of different arrangements is 288 ways.

Since $288 \times 4=1152$ (ways),
there are a total of 1152 different arrangements.
Answer: There are a total of 1152 different arrangements.
Therefore, the correct choice is: A.