# Difference between revisions of "Combinatorics/Introduction"

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− | [[ | + | 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 [[Combinatorics/Intermediate | intermediate]] level. |

− | == | + | == Topics == |

− | + | === Counting === | |

− | + | * Counting [[functions]] | |

− | * [[ | + | ** [[Factorial]] |

− | * [[ | + | ** [[Permutation]] |

− | * [[ | + | ** [[Combination]] |

− | * [[ | + | * [[Casework]] |

− | * [[ | ||

* [[Complementary counting]] | * [[Complementary counting]] | ||

− | |||

* [[Constructive counting]] | * [[Constructive counting]] | ||

+ | * [[Overcounting]] | ||

* [[Committee forming]] | * [[Committee forming]] | ||

− | * [[ | + | * [[Distinguishability]] |

+ | === Probability === | ||

+ | * Counting techniques in probability | ||

+ | * [[Geometric probability]] | ||

+ | * [[Expected value]] | ||

+ | === Miscellaneous === | ||

* [[Combinatorial identities]] | * [[Combinatorial identities]] | ||

− | * [[ | + | ** [[Pascal's triangle]] |

− | + | ** [[Block walking]] | |

− | + | * [[Binomial theorem]] | |

− | |||

− | |||

− | == | + | == Resources == |

=== Books === | === Books === | ||

− | * | + | * [https://artofproblemsolving.com/store/item/intro-counting AoPS Introduction to Counting & Probability Book] |

=== Classes === | === Classes === | ||

− | * [[AoPS Online School/Introduction to Counting & Probability Course |Introduction to Counting & Probability]] | + | * [[AoPS Online School/Introduction to Counting & Probability Course |AoPS Introduction to Counting & Probability Course]] |

+ | |||

+ | === Videos === | ||

+ | * [https://artofproblemsolving.com/videos/counting AoPS Counting & Probability Videos] | ||

+ | * [https://www.youtube.com/watch?v=t6a4uHEwQnM&list=PLT9bNzqjDoMmMNsMAJ3g7C4ptRnPMMrpT Sohil Rathi AMC8 Math Competition Preperation Playlist] | ||

== See also == | == See also == | ||

− | * [[Combinatorics/Intermediate | Intermediate | + | * [[Combinatorics/Intermediate | Intermediate combinatorics]] |

− | * [[Combinatorics/Olympiad | Olympiad | + | * [[Combinatorics/Olympiad | Olympiad combinatorics]] |

+ | [[Category:Combinatorics]] | ||

[[Category:Introductory Mathematics Topics]] | [[Category:Introductory Mathematics Topics]] | ||

− |

## Latest revision as of 21:59, 26 May 2021

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.

## Contents

## Topics

### Counting

- Counting functions
- Casework
- Complementary counting
- Constructive counting
- Overcounting
- Committee forming
- Distinguishability

### Probability

- Counting techniques in probability
- Geometric probability
- Expected value