Question

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.)

Answer 1

To calculate the number of ways to arrange 6 people around a circular table with 7 seats, divide the total number of arrangements by the number of rotations. The number of ways is 102.

Step-by-step explanation:

To calculate the number of ways to arrange 6 people around a circular table with 7 seats, we can use the concept of circular permutations. Since rotations of the same seating arrangement are considered the same, we need to divide the total number of arrangements by the number of rotations (which is 7).

We can start by fixing one person in a seat (let's call it Seat 1). Now, we have 6 people and 6 seats left to arrange. The number of ways to arrange those 6 people in the remaining seats is given by 6!.

However, we need to divide this by 7 to eliminate the redundant arrangements due to rotations. Therefore, the number of ways to arrange 6 people around a circular table with 7 seats is 6!/7 = 720/7 = 102.86 (rounded to the nearest whole number). So, there are 102 ways to arrange the people.