2020 VJC P2 Q6

A group of \(8\) people consists of \(4\) boys and \(4\) girls.

1. They go to a theatre and sit in the last row of \(10\) adjacent seats at random.
   1. Find the number of ways in which they can be seated if they are not all seated together.[2]
   2. Given that they are not all seated together, find the probability that the boys are seated together and the girls are also seated together.[2]
2. At a dinner, the group sits around a square table which has two seats on each side.
   1. Find the number of ways in which they can be seated.[2]
   2. Find the number of ways in which they can be seated if there must be a boy and a girl on each side of the table.[3]
   3. There are \(3\) different desserts on the menu and every one selects a dessert each. Find the number of different selections that can be made by the group.[1]