Seating 8 people at a round table can be solved using the concept of circular permutations. In a circular permutation, the order of arrangement matters, but the starting point is considered fixed.

To find the number of ways to seat 8 people at a round table, we can consider one person as a fixed reference point. We can fix one person at the table and arrange the remaining 7 people around him/her.

The number of ways to arrange 7 people in a line can be calculated as 7!. However, in a circular arrangement, the starting point is fixed, so we need to divide this number by the number of rotations to get unique arrangements.

Here are the steps to calculate the number of ways to seat 8 people at a round table:

1. Fix one person as a reference point.
2. Arrange the remaining 7 people in a line: 7!
3. Divide the result by the number of rotations (8) to account for the fixed starting point: 7! / 8 = 5040 / 8 = 630.

Therefore, there are 630 unique ways to seat 8 people at a round table. However, since the table is round, each arrangement can be rotated 8 times to get the same arrangement. So, we need to divide the result by 8 to eliminate the duplicates.

Final Answer:
630 / 8 = 78

Therefore, there are 78 unique ways to seat 8 people at a round table.

The correct answer is option A) 78.