2020 SJI P2 Q9

A total of \(8\) students are randomly selected from three tutorial groups (TGs) to attend a focused group discussion. There are \(14\) students in each TG.

1. Find the number of ways in which the students can be selected, if there are at least \(2\) students from each TG.[5]

Xiaoming and Ali are among the \(8\) students selected. The room for the focused group discussion has a large table in the middle with \(4\) seats on either side of the facilitator, as shown below.

2. Find the number of ways in which the \(8\) students can be seated if
   1. Xiaoming refuses to sit on any of the \(4\) corner seats and Ali insists on sitting next to him,
   2. Xiaoming refuses to sit on any of the \(4\) corner seats and Ali insists on sitting next to him but not on the seat adjacent to the facilitator.[7]