2023 ASRJC P2 Q8

Some MRT trains have cars featuring \(12\) seats each. Passengers take the trains to travel from station to station each day.

Seats located nearest to the train doors are labelled as priority seats reserved for vulnerable commuters, namely those who are pregnant, elderly, with infants, or the differently-abled. Anyone can sit at the priority seats if there are sufficient seats for all vulnerable commuters in the car.

For one trip, \(12\) passengers, of which \(4\) are vulnerable commuters, got onto Car \(\mathrm{B}\) at the first station.

1. Given that all the vulnerable commuters are seated at priority seats, find the total number of ways all the \(12\) passengers can all sit in Car \(\mathrm{B}\).[2]
2. Find the number of ways the \(12\) passengers can be seated in Car \(\mathrm{B}\) if
   1. two particular girls are seated in the same row but not beside each other.[3]
   2. exactly \(4\) of the \(5\) girls are seated together.[4]