2022 HCI P2 Q8

A school canteen committee consists of \(4\) parents, \(2\) student leaders and \(4\) teachers, chosen from \(10\) parents, \(5\) student leaders and \(8\) teachers.

1. There is a married couple amongst the \(10\) parents. How many different canteen committees can be formed if the couple cannot serve on the committee together?[3]

The school canteen committee of \(10\) members has been formed.

2. All members are to stand in a row to take a group photo with the Vice-Principal. Find the number of arrangements such that the Vice-Principal stands at the centre, both ends of the row are occupied by the students’ leaders, and no two parents stand next to each other.[3]
3. The committee members, together with the Vice-Principal, are seated at a round table with \(11\) chairs during lunch time. Find the probability that the parents are seated together and the teachers are separated.[3]