Probabilistic method

The probabilistic method is a technique used in mathematics and computer science to demonstrate the existence of a certain object or structure by showing that the likelihood of it occurring is greater than zero. Instead of constructing the object directly, researchers calculate the probability that a random selection from a larger set meets specific criteria. If this probability is positive, it implies that such an object must exist, even if we can't explicitly find it. This method is commonly used in combinatorics, algorithm design, and various fields where exact solutions are difficult to derive.