# 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 $S_X$