2023 RVHS P2 Q7

A group of \(8\) people consisting of \(2\) children, \(4\) women and \(2\) men goes for lunch, photo-shoot and a game

1. At lunch, they are seated at a round table such that each child is seated between \(2\) women and no men are seated together. Find the number of ways they can sit.[3]
2. After lunch, they go for a photo-shoot. They stand in a row such that all the women are in descending order of height, from their left to right. Find the number of ways they can stand, assuming that all the women are of distinct height.[2]
3. After the photo-shoot, they are split into \(2\) teams to play a board game. Each team consists of a child, \(2\) women and a man. Find the number of ways the \(2\) teams can be formed.[2]