2020 HCI P2 Q7

A team of \(15\) students was selected for an outdoor education trip. One student volunteered to be the trip leader while another volunteered as the assistant trip leader. They decided to have some ice-breaker games, where all \(15\) students sat in a circle.

1. Find the probability that both leaders were not seated together.[2]

During the ice-breaker games, it was realised that \(3\) of the other \(13\) students belonged to the same class.

2. Find the probability that none of these three students sat next to each other, given that both leaders were not seated together.[3]
3. After the ice-breaker games, both leaders decided to break the team up into two groups to discuss about administrative matters and training program for the trip. The group which discussed about the training program consisted of \(7\) students. Find the probability that the trip leader was heading the training program group while the assistant leader was in charge of the administrative matters group.[2]