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.
(a)
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.
(b)
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]
(c)
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]
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