Combinatorics

Combinatorics is a stream of mathematics that concerns the study of finite discrete structures. It deals with the study of permutation and combination, enumerations of the sets of elements. It characterizes Mathematical relations and their properties.

Mathematicians uses the term “Combinatorics” as it refers to the larger subset of Discrete Mathematics.  It is frequently used in computer Science to derive the formulas and it is used for the estimation of the analysis of the algorithms. In this article, let us discuss what is combinatorics, its features, formulas, applications and examples in detail.

Features of combinatorics

Some of the important features of the combinatorics are as follows:

• Counting the structures of the provided kind and size.
• To decide when particular criteria can be fulfilled and analyzing elements of the criteria, such as combinatorial designs.
• To identify “greatest”, “smallest” or “optimal” elements, known as external combinatorics.

Combinatorial structures that rise in an algebraic concept, or applying algebraic techniques to combinatorial problems, known as algebraic combinatorics.

What are permutation and Combination?

In English, we make use of the word “combination” without thinking if the order is important. Let’s take a simple instance.

The fruit salad is a combination of grapes, bananas, and apples. The order of fruits in the salad does not matter because it is the same fruit salad.

But, let us assume that, the combination of a key is 475. You need to take care of the order, since the other combinations like 457, 574, or others won’t work. Only the combination of 4 – 7 – 5 can unlock.

Hence, to be precise;

• When the order does not have much impact, it is said to be a combination.
• When the order does have an impact, it is said to be a permutation.