When seating people around a round table, we usually account for rotational symmetry, meaning that rotating the entire arrangement doesn’t create a new seating arrangement.

For $n$ people seated around a round table, the number of distinct seating arrangements is:

$(n - 1)!$

This is because fixing one person (to eliminate rotational symmetry) leaves $n-1$ people to arrange.

In this case, for 8 students, the number of ways they can be seated around the table is:

$(8 - 1)! = 7! = 5040$

So, there are 5040 ways to seat 8 students around a round table.

Would you like a deeper explanation on how this formula works or have any other questions?

Here are 5 related questions for further exploration:

1. How many ways can 10 students be seated around a round table?
2. What if the 8 students need to be seated in a straight line instead of a round table?
3. How many ways can the 8 students be seated around a round table if two specific students must sit next to each other?
4. How many distinct seating arrangements are there if the 8 students are split into two equal groups at two round tables?
5. How would the number of seating arrangements change if the table was rectangular instead?

Tip: When calculating permutations or combinations in circular arrangements, always consider whether rotational symmetry matters!