Combinatorics is an area of mathematics which is concerned with counting and arranging. It applies mathematical theories and operations to count quantities that are much too difficult to be counted by conventional methods.
Especially useful in computer science, combinatorics methods can be used to develop a rough idea of how many operations a computer algorithm will require. This area of mathematics is also important when studying discrete probability, as it can be used to count possible outcomes in a uniform, probability experiment.
As mentioned previously, combinatorics can also be used with how things are arranged, and by ‘arranged’ we mean how objects can be grouped together. The basic rules surrounding arrangement are the rule of product and the rule of sum, which dictate how to count arrangements using both multiplication and addition.
The rule of product, using multiplication, states that if there are X ways to arrange something and Y ways to arrange something else after that, then the equation to arrange both of those things are X x Y.
The rule of sum, using addition, also states that if there are X ways to arrange something, and there are Y ways to arrange something else but both arrangements clash and this cannot happen, the equation to arrange either of these things is X + Y.
Within combinatorics, graphs are used frequently, and the application of graphs within this area of mathematics is called graph theory. It’s concerned with different types of networks called “points connected by lines” – they are not the graphs of analytic geometry. The terminology within graph theory for the axes are vertex for a point and edge for a line.
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