How many ways can 12 students be seated around a circular table
3. How many ways can 12 students be seated around a circular tables
To calculate the number of ways 12 students can be seated around a circular table, we need to consider the concept of circular permutations.
For a fixed seating arrangement, we can assume one student as the "starting point" and arrange the remaining 11 students around the table. The number of ways to arrange the remaining students in a line would be (11!). However, in a circular arrangement, any rotation of the students would result in the same arrangement.
Since there are 12 starting points (one for each student), we need to divide the total number of linear arrangements by 12 to eliminate the repetitions.
Therefore, the total number of ways the 12 students can be seated around the circular table is:
(11!) / 12 = 39,916,800 / 12 = 3,326,400 ways.