In this thesis we will get to know the basics of combinatorics and probability, and their connection to and appliance in not only in everyday life but also in many fields of science. The first part deals with combinatorics that is crucial to understanding probability. Combinatorics is a branch of mathematics connected with other branches of mathematics, such as probability theory. The second part of the thesis deals with the basics of probability. Examples show that without knowing the probability theory, the description of many social and natural events would be impossible. This is a branch of mathematics dealing with describing different models in which uncertainties occur. Events that may or may not happen are observed through the probability theory. The basic terms of the probability theory are the event and its probability.