Mathematics | PnC and Binomial Coefficients

Combinatorics

Last Updated : 07 Apr, 2025

Combinatorics is the branch of Mathematics dealing with the study of finite or countable discrete structures. It includes the enumeration or counting of objects having certain properties. Counting helps us solve several types of problems such as counting the number of available IPv4 or IPv6 addresses.

Permutation and Combination are fundamental concepts in combinatorics that help us solve problems involving arrangements and selections. While permutation deals with arranging objects in a specific order, combination focuses on selecting objects without considering the order.

Combinatorics-in-mathematics-copy

Permutation and Combination for Students and Beginners

This section introduces basic concepts like factorial, permutations, and combinations with easy explanations for new learners.

Permutation and Combination for Aptitude Preparation

Practice aptitude-style problems and quizzes to prepare for competitive exams using permutations and combinations.

Advanced Topics of Permutation and Combination

Explore deeper topics like permutation groups, their properties, and related theorems in advanced combinatorics.

Permutation and Combination for Programmers

This section covers coding problems based on permutations and combinations, helping you implement logic and solve real-world programming challenges.

Mathematics | PnC and Binomial Coefficients

C

Chirag Manwani

Improve

Article Tags :

Practice Tags :

Misc

Similar Reads

Discrete Mathematics | Representing Relations

Prerequisite - Introduction and types of Relations Relations are represented using ordered pairs, matrix and digraphs: Ordered Pairs - In this set of ordered pairs of x and y are used to represent relation. In this corresponding values of x and y are represented using parenthesis. Example: {(1, 1),

Representation of Relation in Graphs and Matrices

Understanding how to represent relations in graphs and matrices is fundamental in engineering mathematics. These representations are not only crucial for theoretical understanding but also have significant practical applications in various fields of engineering, computer science, and data analysis.

Closure of Relations

Closure of Relations: In mathematics, especially in the context of set theory and algebra, the closure of relations is a crucial concept. It involves extending a given relation to include additional elements based on specific properties, such as reflexivity, symmetry, and transitivity. Understanding

Number of possible Equivalence Relations on a finite set

An equivalence relation is defined as a relation that is Reflexive, Symmetric, and Transitive. Before we explore how to calculate the number of possible equivalence relations on a set âˆ£Aâˆ£ = n, letâ€™s first look at an example of an equivalence relation and identify its equivalence classes.Example of a

Classes of Functions | Injective, Surjective and Bijective Functions

Classes of Functions: Functions are fundamental in mathematics and have wide-ranging applications in engineering, computer science, and various other fields. Understanding the different classes of functionsâ€”injective, surjective, and bijectiveâ€”is essential for analyzing mathematical models and solvi

Mathematics | Total number of Possible Functions

In this article, we are discussing how to find a number of functions from one set to another. For understanding the basics of functions, you can refer to this: Classes (Injective, surjective, Bijective) of Functions.Â Number of functions from one set to another: Let X and Y be two sets having m and n

Discrete Maths | Generating Functions-Introduction and Prerequisites

Discrete Maths | Generating Functions-Introduction and PrerequisitesPrerequisite - Combinatorics Basics, Generalized PnC Set 1, Set 2 Definition: Generating functions are used to represent sequences efficiently by coding the terms of a sequence as coefficients of powers of a variable (say) \big x in

Mathematics | Generating Functions - Set 2

Prerequisite - Generating Functions-Introduction and Prerequisites In Set 1 we came to know basics about Generating Functions. Now we will discuss more details on Generating Functions and its applications. Exponential Generating Functions - Let h_0, h_1, h_2, ........., h_n, ...... e a sequence. The

Mathematics | Sequence, Series and Summations

Sequences, series, and summations are fundamental concepts of mathematical analysis and it has practical applications in science, engineering, and finance.Table of ContentWhat is Sequence?Theorems on SequencesProperties of SequencesWhat is Series?Properties of SeriesTheorems on SeriesSummation Defin

Mathematics | Independent Sets, Covering and Matching

Mathematics | Independent Sets, Covering and Matching1. Independent SetsA set of vertices I is called an independent set if no two vertices in set I are adjacent to each other in other words the set of non-adjacent vertices is called an independent set.It is also called a stable set.The parameter Î±0