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

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28