How many ways can we connect $3$ yellow balls, $2$ blue and $1$ green, according to the following rule?
- Yellow Balls ("A" elements) make up to 1 link
- Blue Balls ("B" elements) make up to 2 links
- Green Balls ("C" elements) make up to 3 links
Consider also:
- The balls may or may not connect;
- The balls are spread out in space, so do not consider fixed positions (what matters are the connections and not the positions)!
- Rotations and reflections of connections between the same elements are considered the same!
The problem is illustrated in the figure below:
To better understand the question, follow a simpler example in the figure below:
Remembering that:
Is it a combination problem? Is there a formula or analytical method to solve this type of problem? Does anyone have any ideas?