2022 NJC J2 CT P2 Q2

Nine students from a particular CCA have to arrange themselves for a photo-shoot. They are to stand only on the spots labelled O, where the X’s are markings on the ground.

How many ways can these nine students be arranged such that two particular students from this group, Jason and Jay Jay, cannot be standing next to each other?[4]

These nine students went to the canteen for a meal after the photo-shoot. There are two round tables available and they need to split into \(2\) groups, comprising \(1\) group of four and \(1\) group of five, to occupy the tables. Jason and Jay Jay do not want to be seated at the same table while another three particular students want to be seated next to one another. How many ways are there to arrange these nine students in the two round tables for a meal?[4]