Combinatorics is a branch of mathematics that deals with counting, arranging, and selecting objects. It studies finite discrete structures and helps in solving problems related to enumeration.
The two main concepts of combinatorics are the following:
- Permutation refers to the arrangement of objects where the order is important.
- Combination refers to the selection of objects where the order is irrelevant.
Combinatorics plays an important role in computer science, probability, and algorithm analysis.
For Beginners
This section introduces basic concepts like factorials, permutations, and combinations with straightforward explanations for new learners.
- Factorial
- Fundamental Counting Principle
- Permutation
- Permutation Formulas
- Combination
- Combination Formulas
- Permutations vs Combinations
- Principle of Inclusion and Exclusion
- Real-Life Applications
Aptitude Preparation
Practice aptitude-style problems and quizzes to prepare for competitive exams using permutations and combinations.
- Aptitude Questions and Answers
- Problem on P & C - set 1 | set 2
- Problems On Permutations | Set 1
- Permutation and Combination- Quiz
Advanced Topics
Explore deeper topics like permutation groups, their properties, and related theorems in advanced combinatorics.
- Permutation Groups and Multiplication of Permutation
- Inverse of Permutation Group
- Order of Permutation Group
- Even and Odd Permutations and their theorems
For Programmers
This section covers coding problems based on permutations and combinations, helping you implement logic and solve real-world programming challenges.
- Program to calculate value of nCr using Recursion
- Permutations of given String
- All Permutations of an Array
- Ways to sum to N using Natural Numbers up to K with repetitions allowed
- Count all possible N-length vowel permutations
- Generate a combination of minimum coins
- Number of ways to go from one point to another in a grid
- Different ways to represent N as sum of K non-zero integers
- Number of arrays of size N whose elements are positive integers and sum is K
- Generate all cyclic permutations of a number