Combinatorics/Introduction

An introduction to combinatorics primarily involves counting and probability. As problem-solving ability improves, the scope of combinatorics grows, leading students to the intermediate level.

Topics

Counting

• Counting functions
  • Factorial
  • Permutation
  • Combination
• Common stragegies
  • Casework
  • Complementary counting
  • Constructive counting
  • Overcounting
• Committee forming
• Distinguishability

Probability

• Probability techniques
  • Addition and product rules
  • Complementary probability
• Geometric probability
• Expected value

Miscellaneous

• Combinatorial identities
  • Pascal's triangle
  • Block walking
• Binomial theorem

Introductory combinatorics resources

Books

• the Art of Problem Solving: Introduction to Counting and Probability by David Patrick (details)

Classes

• Introduction to Counting & Probability (information page)

Videos

• AMC8 Math Competition Preperation Playlist by Sohil Rathi
• AoPS Counting & Probability Videos

See also

• Intermediate topics in combinatorics
• Olympiad topics in combinatorics