2011 MJC MYCT P2 Q6

Tom and his friend Mary are going out for dinner with their parents at a restaurant. Find the number of ways that the \(6\) of them can be seated at a round table of \(6\) if

1. each family is to be seated together, [2]
2. only their parents need to be seated with their respective spouses.[2]

When they arrive at the restaurant, the waiter informs them that there are only \(2\) round tables of \(3\) available.

3. Find the number of ways that they can be seated if there are no restrictions on the seating arrangement.[2]

TGM seating convention: rotations of a seating around a table count as the same arrangement, while reflections count as different. In part (iii), the two tables are indistinguishable: exchanging the two seated groups does not create a new arrangement.