Combinatorics/Introduction

An introduction to combinatorics concerns mostly counting and probability. As problem-solving ability becomes more advanced, the scope of combinatorics grows, leading students to the intermediate level.

Topics

Counting

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

Probability

• Counting techniques in probability
• Geometric probability
• Expected value

Miscellaneous

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

Resources

Books

• AoPS Introduction to Counting & Probability Book
• Ritvik Rustagi's ACE The AMC 10 and AMC 12 book has a chapter on combinatorics.

Classes

• AoPS Introduction to Counting & Probability Course

Videos

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

See also

• Intermediate combinatorics
• Olympiad combinatorics