2024 IGCSE Additional Mathematics May/June 0606/21 Q5

There are \(3\) women, \(2\) men and \(4\) children in a choir.

1. The choir stands in a single straight line.
   1. Find the number of possible arrangements if the first person and last person are both women.[2]
   2. Find the number of possible arrangements if all the children stand next to each other.[2]
2. Four of the choir are selected to sing in a group.
   1. Find the number of different selections if no man is chosen.[2]
   2. Find the number of different selections if at least \(2\) women are chosen.[2]