Name: Lori
Level: 11th grade
Asked by: OAT exam

Question: How many arrangements can 6 people be seated round a circular table?

Answer: 120

I Used the formula n!/(n-r)! and didn't get the right response.

Lori

Think of the table sitting in a place where you can only see the table and chairs, and the chairs are identical. Each person can only see the order around the table but no reference to anything outside the table.

Start seating the people. The first person can be seated anywhere since there is no difference in the chairs. Once that person is seated there are 5 choices for the person to put on her left. Having seated the second person there are 4 choices as to who goes on her left. Continuing in this way there are 3 choices as to who is seated on the left of the third person, and so on. Hence altogether there are 54321 = 120 wys to seat the people around the table.