Probablistic methods as a proof technique

The probabilistic method is a nonconstructive method, primarily used in combinatorics, was pioneered by Paul Erdös, for proving the existence of a prescribed kinds of mathematical objects. Suppose we want to show that an object of a specific class with a certain property exists. Often it might be difficult to show the existence by explicitly constructing such an object. In the light of this difficulty, the main idea of probabilistic method is that if one randomly chooses objects from a specified class, such that the probability of the result having the said property is more than zero, then an object with the said property exists! Note that although the proof uses probability, the final conclusion is determined for certain. In this article, we demonstrate the use of probabilistic methods using two problems as described in sections 2 and 3.