In a cube with 12 edges, what method can be used to determine valid selections of 3 edges to paint without hitting corners?

The correct choice is indeed centered around combination formulas, which are essential in determining valid selections of edges without hitting corners in a cube.

In a cube, there are 12 edges, and the goal here is to select 3 edges such that no two selected edges meet at a vertex. This scenario can be effectively analyzed using combination concepts because the order of selection does not matter; rather, it is about choosing groups of edges.

When applying combination formulas, you focus on selecting groups from a larger set without regard to the sequence in which they are chosen. This is particularly useful in scenarios involving geometric shapes like cubes, where specific combinations need to be identified that meet certain conditions, such as not sharing a vertex.

To enforce the condition of avoiding corners, one must understand the cube's structure: each edge is connected to two other edges. As you select edges, you need to ensure that you are considering only those that do not connect to each other. This is fundamentally what combination formulas enable you to manage efficiently.

Utilizing combination calculations allows for a systematic selection process. By applying the appropriate mathematical combinations, one can easily calculate the number of viable groups of edges that fulfill the criteria of the task, emphasizing the strength of combinatorial reasoning in such geometric problems