Permutations and Combinations


1

Introduction

An introduction to Permutations and Combinations

2

Fundamental Principle of Counting: Part 1

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.

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