Counting Techniques and Combinations

When we attempt to calculate the probability of a future occurrence, we must first map the entirety of what is possible. Counting, in the mathematical sense, is not merely tallying objects one by one; it is the systematic unearthing of hidden structures within sets of choices. It is the geometry of branching paths. Before we can determine how likely an event is, we must rigorously define the boundaries of the universe in which that event takes place.