The law of combinations applies when there are many interacting people or objects. Suppose, for example, that we have a class of 30 students. They can interact in various ways. They can work as individuals: there are 30 of them; they can work in pairs—there are 435 different pairs; they can work in triples—there are 4,060 possible different triples; and so on, up to, of course, them all working together—there is one set of all 30 students working together.
In total, the number of different possible groups of students that could be formed is 1,073,741,823. That’s more than a billion, all just from 30 students. In general, if a set has n elements, there are 2n − 1 possible subsets that could be formed. If n = 100, the result is 2100 − 1, which is approximately equal to 1030, a truly large number in anyone’s terms.
But if even 1030 isn’t large enough for you, consider the implications of the World Wide Web, which has around 2.5 billion users, any and all of whom can interact with any of the others. This gives 3 × 1018 pairs and 10750,000,000 possible groups of interacting members. Even events with very small probabilities become almost certain if you give them that many opportunities to happen.