## 1 | ## Introduction | An introduction to Permutations and Combinations |

## 2 |
| An introduction to the fundamental principles of counting |

## 3 | ## Fundamental Principle of Counting: Part 2 | An introduction to the Multiplication Principle |

## 4 | ## Fundamental Principle of Counting: Part 3 | An introduction to the Addition Principle |

## 5 | ## Fundamental Principle of Counting: Part 4 | Combined usage of the Multiplication Principle and the Addition Principle |

## 6 | ## Fundamental Principle of Counting: Examples | A few examples to illustrate the multiplication and the addition principles of counting. |

## 7 | ## Permutations | Establishment of notations and formulas for factorials and permutations – n! and nPr |

## 8 | ## Permutations: Examples | A few examples related to permutations, particularly those involving nPr. |

## 9 | ## Circular Permutations | Permutations of distinct objects in a circle, or circular permutations. |

## 10 | ## Circular Permutations: Examples | A few examples related to circular permutations of distinct objects |

## 11 | ## Combinations: Part 1 | Number of selections or combinations of r objects out of n distinct objects. Derivation of nCr or C(n, r) |

## 12 | ## Combinations: Part 2 | An alternate method to derive the formula nCr for combinations. |

## 13 | ## Combinations: Part 3 | Proof of the result C(n,r) = C(n,n-r) using formula as well as combinatorial argument. |

## 14 | ## Combinations: Examples | A few examples to illustrate the use of nCr in combinatorial problems |

## 15 | ## Combinations: Examples | A few more examples to illustrate the use of nCr in combinatorial problems |

## 16 | ## Permutations of Identical Objects: Part 1 | Permutations of objects in a row, of which some are identical. |

## 17 | ## Permutations of Identical Objects: Part 2 | Permutations of objects in a row, of which some are identical. |

## 18 | ## Permutations of Identical Objects: Examples | A few examples illustrating permutations of identical objects |

## 19 | ## Combinations of Identical Objects | A brief overview of combinations or selections involving Identical objects. |

## 20 | ## All Possible Selections: Part 1 | Selection of any number of objects from a collection of n distinct objects |

## 21 | ## All Possible Selections: Part 2 | Selection of any number of objects from a collection of n distinct objects |

## 22 | ## All Possible Selections: Part 3 | Selection of any number of objects from a collection of n identical objects |

## 23 | ## All Possible Selections: Examples | Examples relating to all possible combinations |

## 24 | ## Divisors of a Number | Derivation of the formula for calculating the number of divisors of a number. |

## 25 | ## Divisors of a Number: Examples | Examples illustrating calculation of the number of divisors of a number. |

## 26 | ## Division into Groups: Part 1 | Division of different objects into groups of fixed sizes. |

## 27 | ## Division into Groups: Part 2 | Division of different objects into groups of fixed sizes, where group sizes are identical. |

## 28 | ## Division into Groups: Examples | A few solved examples illustrating the division of distinct objects into groups of fixed sizes. |