2025 NJC P2 Q7

A toy train is made up of \(3\) types of train units: engine, carriage, and wagon. There are \(4\) identical engines \((E)\), \(3\) identical carriages \((C)\), and \(2\) identical wagons \((W)\).

1. All the train units are placed in a line such that either the first unit is an engine or the last two units are engines, or both. Find the number of ways to form the toy train.[4]

2. For another kind of toy train, all the train units are placed in a line such that the first train unit is an engine and all the carriages are in front of the wagons. An example of such a toy train would be:

   \( E \ C \ C \ E \ E \ C \ W \ E \ W \).

   Find the number of ways to form the toy train.

   [3]