* A branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs andmatroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and studying combinatorial structures arising in analgebraic context, or applying algebraic techniques to combinatorial problems (algebraic combinatorics).
* The branch of mathematics studying the enumeration, combination, and permutation of sets of elements and the mathematical relations that characterize their properties.
PROBABILITY OR LIKELIHOOD
* A measure or estimation of how likely it is that something will happen or that a statement is true. Probabilities are given a value between 0 (0% chance or will not happen) and 1 (100% chance or will happen). The higher the degree of probability, the more likely the event is to happen, or, in a longer series of samples, the greater the number of times such event is expected to happen.
* The study of graphs, which are mathematical structures used to model pair wise relations between objects from a certain collection. A "graph" in this context is a collection of "vertices" or "nodes" and a collection of edges that connect pairs of vertices. A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another; see graph (mathematics) for more detailed definitions and for other variations in the types of graph that are commonly considered. Graphs are one of the prime objects of study in discrete mathematics.
* A branch of mathematics concerned about how networks can be encoded and their properties...