### Instruction: How many ways are there to arrange 6 people around a circular table with 7 seats?  (Two seatings are considered the same if one is a rotation of the other.).### Response: To arrange 6 people around a circular table with 7 seats, I need to choose one seat to leave empty and then arrange the 6 people in the remaining seats.
Since the table is circular, I can fix the empty seat as a reference point and then count the ways to arrange the 6 people relative to that seat.
This is equivalent to arranging 6 people in a row, which can be done in 6! ways.
Therefore, the total number of ways to arrange 6 people around a circular table with 7 seats is 6!.