2024 ACJC H1 Q11

A family of \(7\), consisting of a father, mother, \(2\) sisters, and \(3\) brothers is queuing in a line.

1. Find the number of different possible arrangements
   1. if the sisters stand next to each other and the brothers are all next to each other.[2]
   2. if either the father is first in the queue or mother is last in the queue (or both).[3]

2. The family is queuing in a line in a random order. Find the probability that no two brothers stand next to each other.[3]