2023 NJC P2 Q7

The Ang family, the Bao family and the Chew family have three, five and four members respectively. The three families are invited to a wedding dinner.

Due to venue constraints, only \(2\) members from each family can attend the dinner.

1. Find the number of ways to select the \(6\) attendees.[1]
2. The \(6\) attendees selected in part (a) are randomly arranged to sit at a round table. Find the probability that the \(2\) members from the Ang family are not next to each other.[3]

The host decides to change the layout of the venue to accommodate more people, so that a total of \(7\) people can now attend the dinner.

3. Find the number of ways to select the \(7\) attendees with at least \(2\) members from each family.[3]
4. The \(7\) attendees selected in part (c) are randomly arranged to sit in a row during photo-taking. Find the probability that the people from the same family are seated together.[2]