2025 JPJC P2 Q5

In a strategy game called \(\mathit{Colour\ Clash}\), players draw coloured orbs from a magical pouch to determine their elemental powers. The pouch contains:

• \(5\) red orbs (Level \(1\) to \(5\)),
• \(4\) blue orbs (Level \(1\) to \(4\)),
• \(3\) green orbs (Level \(1\) to \(3\)).

Orbs of the same colour are non-identical with each same-coloured orb representing a different level.

A player randomly draws four orbs without replacement at the start of the game. Given that the order in which the orb is drawn is not relevant, find the number of ways this can be done such that

1. there are no restrictions,[1]
2. there are at least two colours present,[2]
3. at least one orb of each colour is drawn.[3]