2024 VJC P2 Q5

Two married couples, two single adults and two children form a team of \(8\) to take part in a series of games.

1. In the first game, the team sits in a circle. Find the number of arrangements that can be formed if each married couple must be seated together.[2]
2. A group of \(3\) people are to be selected from the team for the second game. Find the number of different groups that can be formed if there must not be a married couple in the group.[2]
3. In the third game, each team member selects a unique number from the set \(\left\{ 1,2,\ldots ,8 \right\}\). Find the number of different ways this can be done if the numbers selected by the children are both greater than the numbers selected by the two single adults.[2]