In how many ways can 10 people be seated across two tables, each seating five people?

To understand this problem, we need to first break it down. Assuming the tables are round, we can notice that this is a circular arrangement question.

We first need to assign five from a group of 10 people to a table. Since we don't care who appears on that table, we can use the notation:



However, since they are not distinct tables, then we would have overcounted by a factor of 2!, since there are two tables. Thus, the total number of ways to assign the tables is:



Now, we need to consider the total number of ways to arrange the people in each table. Since they are circular, then each table can be arranged in 4! ways.