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 2^{n} − 1 possible subsets that could be formed. If n = 100, the result is 2^{100} − 1, which is approximately equal to 10^{30}, a truly large number in anyone’s terms.
But if even 10^{30} 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 × 10^{18} pairs and 10^{750,000,000} possible groups of interacting members. Even events with very small probabilities become almost certain if you give them that many opportunities to happen.