| 30 | Everyone shakes hands | Easy | Lemma | Counting pairsAvoiding double counting | |
| 43 | Every subset | Easy | Lemma | Powers of twoIndependent choices | |
| 44 | Choosing a pair | Easy | Lemma | Combinationsn choose 2 | |
| 603 | Four different digits | Easy | Lemma | Counting | |
| 604 | Licence plates | Easy | Lemma | Counting | |
| 605 | Around a table | Easy | Lemma | Counting | |
| 606 | Anagrams of BANANA | Easy | Lemma | Counting | |
| 607 | President and vice-president | Easy | Lemma | Counting | |
| 609 | Walking on a grid | Easy | Lemma | Counting | |
| 610 | Diagonals of a decagon | Easy | Lemma | Counting | |
| 800 | Arranging MISSISSIPPI | Easy | Lemma | Counting | |
| 848 | Consonant‑vowel selection | Easy | Hall & Knight | permutationscombinations | |
| 849 | Scholarship assignments | Easy | Hall & Knight | product rule | |
| 850 | Arrangements of equation | Easy | Hall & Knight | permutations | |
| 853 | Changes with five bells | Easy | Hall & Knight | permutations | |
| 854 | Changes with seven bells, tenor fixed | Easy | Hall & Knight | permutations with restriction | |
| 856 | Council and Alderman Committee | Easy | Hall & Knight | combinationsmultinomial | |
| 857 | Combinations of Fifty Choose Forty‑Six | Easy | Hall & Knight | binomial coefficient | |
| 859 | Selecting a Party | Easy | Hall & Knight | combinationssubsets | |
| 865 | Allocating volunteers to districts | Easy | Hall & Knight | multinomialallocation | |
| 866 | Books on a shelf with English in middle | Easy | Hall & Knight | selectionarrangement | |
| 868 | Shelving volumes of works | Easy | Hall & Knight | blocksinternal order | |
| 869 | Best and worst papers apart | Easy | Hall & Knight | complementary counting | |
| 872 | Permutation ratio problem | Easy | Hall & Knight | permutationsalgebraic manipulation | |
| 873 | Flag signal arrangements | Easy | Hall & Knight | permutationssum of series | |
| 874 | Binomial ratio problem | Easy | Hall & Knight | binomial coefficientsalgebraic solving | |
| 879 | Choosing conveyances for three trips | Easy | Hall & Knight | independent choices | |
| 880 | Colourful counter arrangements | Easy | Hall & Knight | permutationsmultiset | |
| 881 | Loading animals onto stalls | Easy | Hall & Knight | choicesexponentiation | |
| 882 | Distributing items to persons | Easy | Hall & Knight | functionsassignments | |
| 883 | Dividing five objects between two people | Easy | Hall & Knight | distributionexclusion | |
| 884 | Permutations of repeated letters | Easy | Hall & Knight | multinomialrepetition | |
| 885 | Unsuccessful letter‑lock attempts | Easy | Hall & Knight | product rulecomplement | |
| 886 | Triangles from a 15‑gon | Easy | Hall & Knight | combinationsgeometric counting | |
| 888 | Numbers below 10000 | Easy | Hall & Knight | base‑8 countingenumeration | |
| 890 | Telegraph signals | Easy | Hall & Knight | exponential countingexclusion | |
| 891 | Drawing money from a bag | Easy | Hall & Knight | subsetsbinary choices | |
| 894 | Flag signalling | Easy | Hall & Knight | subsetspermutations | |
| 904 | Permutation 8P7 | Easy | Hall & Knight | permutations | |
| 905 | Permutation 25P5 | Easy | Hall & Knight | permutations | |
| 906 | Combination 24C4 | Easy | Hall & Knight | combinations | |
| 907 | Combination 19C14 | Easy | Hall & Knight | combinations | |
| 908 | Permutations of triangle | Easy | Hall & Knight | permutations | |
| 909 | Permutations beginning with t and ending with e | Easy | Hall & Knight | permutations | |
| 910 | Choosing four digits | Easy | Hall & Knight | combinationsselection | |
| 911 | Four‑digit numbers | Easy | Hall & Knight | permutationsarrangements | |
| 912 | Choosing watches of four men | Easy | Hall & Knight | combinations | |
| 913 | Watches containing a given man | Easy | Hall & Knight | combinations | |
| 917 | Ring arrangements of seven people | Easy | Hall & Knight | circular permutations | |
| 923 | Arrangements Starting with Capital | Easy | Hall & Knight | permutationsrestricted positions | |
| 924 | Arrangements Starting and Ending with Capital | Easy | Hall & Knight | permutationsrestricted positions | |
| 927 | Committee with Exactly One Officer | Easy | Hall & Knight | combinations | |
| 928 | Committee with At Least One Officer | Easy | Hall & Knight | combinations | |
| 1538 | Multinomial Coefficient 1 | Easy | Hall & Knight | Multinomial TheoremCoefficients | |
| 1539 | Multinomial Coefficient 2 | Easy | Hall & Knight | Multinomial TheoremCoefficients | |
| 1540 | Multinomial Coefficient 3 | Easy | Hall & Knight | Multinomial TheoremCoefficients | |
| 1542 | Trinomial Coefficient 1 | Easy | Hall & Knight | Multinomial TheoremPolynomial Expansion | |