---
title: Combinations
description: Combinations are selections of items from a larger set where the order of selection does not matter. Learners will understand how to calculate and apply binomial coefficients to solve counting problems in probability and statistics.
category: mathematics
subcategory: combinatorics
difficulty: beginner, intermediate, advanced
url: /subject/combinations
---

# Combinations

Combinations are selections of items from a larger set where the order of selection does not matter. Learners will understand how to calculate and apply binomial coefficients to solve counting problems in probability and statistics.

## Available Resources

1 Books • 1 Courses • 3 Websites

## Websites

### 1. Brilliant.org Combinatorics

An interactive Brilliant course on counting, built around short problems with immediate feedback. It covers the rule of product, permutations, combinations, binomial coefficients and casework, so learners can count arrangements and selections without listing them out. Most lessons require a subscription.

**Difficulty:** Beginner | **Price:** Paid

**Link:** https://brilliant.org/courses/combinatorics/

**Tags:** combinatorics, combinations, permutations, counting, binomial-coefficients

### 2. Art of Problem Solving - Combinatorics

The Art of Problem Solving wiki's combinatorics hub, linking concise articles on counting principles, permutations, combinations, the binomial theorem, stars and bars, and inclusion-exclusion, with competition problems. Suited to students preparing for contests such as AMC and AIME.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://artofproblemsolving.com/wiki/index.php/Combinatorics

**Tags:** combinatorics, combinations, counting, competition-math, binomial-theorem

### 3. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

## Courses

### 1. Mathematics for Computer Science (MIT 6.042J)

**Author:** Tom Leighton, Marten van Dijk

Discrete mathematics for computer science with an emphasis on definitions and proofs: logic, induction, sets and relations, graph theory, modular arithmetic, asymptotics, counting and discrete probability. 25 lecture videos, problem sets and exams with solutions build fluency in writing proofs.

**Difficulty:** Intermediate | **Price:** Free

**Link:** https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-fall-2010/

**Tags:** discrete-mathematics, mathematical-proofs, induction, graph-theory, combinatorics, discrete-probability

## Books

### 1. A Course in Combinatorics

**Author:** J.H. van Lint, R.M. Wilson

Graduate-level textbook covering graph theory, designs, codes, Latin squares, partitions, inclusion-exclusion, generating functions and Ramsey theory in short self-contained chapters. Readers learn standard combinatorial proof techniques and can tackle counting and existence problems beyond introductory discrete mathematics.

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/0521422604?tag=edmonddante07-20

**Tags:** books, mathematics-statistics, combinatorics

---

*This content is part of Dantes.io - Your Treasure Map to Knowledge*

*Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).*

View this page online: https://dantes.io/subject/combinations