Interactive pages for Combinatorics

Subsets
Ordered and unordered combinations Examples 1 and 2
The National Lottery Example 4
The binomial expansion Example 5, Theorem 6
Pascal's triangle Propositions 7 and 8
Pascal's identity Proposition 7
Complements Proposition 8
An extension of Pascal's identity Example 16
Grid routes Example 9
Counting solutions to some equations Example 10, Proposition 11
Sum of numbers in a triangle Example 17
Counting subtriangles Example 18
Lines across circles Example 20
Covering a chess board with dominos Example 22
Tetris Example 23
The seven bridges of Königsberg Example 24
Handshaking Example 25
Numbers of hairs Example 26
Sums of subsets Example 27
Modular sums Example 28
Piggy bank Example 29
Tennis and squash Example 30
Tennis, squash and badminton Example 31
Derangements of 1234 Example 33
Derangements of 12345 Example 33
Numbers coprime with 42 Example 34, Theorem 35
Matching problems
Basic rook problems Examples 36, 38 and 40
Rooks and permutations
Rooks and derangements Example 39
Rook polynomial for the full board
Problème des ménages Example 41
Solving the Problème des ménages Example 41
Snap Example 42
Blocking and deleting Theorem 43
Factoring rook polynomials Theorem 46
Staircase
Counting the sets $S_X$