For Santiago's birthday dinner, he and his family sat at a round table. He ate dinner with 7 family members and everyone chose their seats randomly. What is the probability they sat in age order?

Answer 1

Step 1: 8 people can sit randomly around the round table (8-1)! = 7! = 5040 ways.

Step 2: Only 2 arrangements can be in age order (clockwise and counterclockwise).

Step 3: So the probability they sat in age order is 2/7! = .040%, i.e. very unlikely!