Erdős–Lovász Local Lemma

The Erdős–Lovász Local Lemma is a principle in probability and combinatorics that helps show the likelihood of avoiding all "bad" events simultaneously, even if some events are dependent. It states that, under certain conditions where events are not too likely and not too interdependent, there's a positive probability that none of these undesirable outcomes occur at once. Essentially, it provides a way to prove the existence of arrangements or solutions where multiple constraints are satisfied simultaneously, despite potential overlaps in their dependencies, by balancing the probabilities and interactions involved.