1. Permutation of different coloured balls
  2. Number of binary strings not having even-length runs of $0$ or $1$

  3. Number of divisors of the number $2079000$ which are even and divisible by $15$
  4. Shortest Addition Chain to Arrive to $100$

  5. How many ways can hexagonal tiles of side a be arranged in a b*a sided triangle?

  6. Find a distribution and probability.

  7. Combinatorics: choose 10 mathematicians out of $18$ mathematicians and $6$ physicists out of $12$ physicists.

  8. How many ways to add to $50$ with $1, 4$ and $6$
  9. Proof: Generalized Version Of The Basic Counting Principle
  10. Number of Multiples of $a+bi \in \mathbb{Z}[i]$ with bounded norm

  11. Number of ways I can create positive 5-number integers (which are multiples of 5)
  12. Logic using Permutation

  13. Give a combinatorial proof for the identity

  14. What is the $n$-th difference of $\sin(ax)$

  15. Number of ways 6 things can be selected from a group of identical things
  16. Number of graphs on [100n] vertices with degree at most 100

  17. Calculating entropic penalties based on combinatorics

  18. The number of words (finite sequences) up to isomorphism

  19. My Simple Combinatorial Method to Enumerate All Sudoku Solution Grids

  20. Subgroups of $PSL(2,q)$

  21. Colored ball problem combinations distribution

  22. Prove by a combinatorial argument that ${n \choose r}{r \choose s}={n \choose s} {n-s \choose r-s} $

  23. Probability: Find the number of ways to select $5$ clerks from $20$ applicants.
  24. Prove by a combinatorial argument that $(n-r){n \choose r}=n{n-1 \choose r}$
  25. In how many ways can one yellow, two red and four green beads be placed on a bracelet if the beads are identical apart from colour?

  26. Beggar-my-neighbour possible games
  27. How many samples of size $4$ selected from $10$ red and $5$ white numbered marbles have exactly $3$ red marbles?

  28. Determine remainder when N is divided by 1000?

  29. Combinatorics intuition

  30. Ensuring the Multinomial Counting Theorem Produces Integer Coefficients
  31. Number of Unique Positive Integer Solutions

  32. How many combinations of $n$ balls of up to $n$ different colors are there?

  33. Simplification of a Finite Sum

  34. How many distinct games are there on a set of cards?

  35. find $\sum_{k=0}^{n}(-1)^k\binom{n}{k}^2$
  36. In how many ways can we to place an $X$ in four cells, such that there is exactly one $X$ in each row, column, and $2\times2$ outlined box?

  37. How many sets of numbers can we find?
  38. How many ways can I put down two indistinguishable pieces on an ordinary $8 \times 8$ chessboard if they must either be in the same row or column?
  39. How many symmetric oriented graphs with n vertices are there?
  40. Ways of choosing ice-cream scoops - intuition/further explanation

  41. Comparing Binary Matrices and Weights

  42. A seemingly simple composite induction (pun intended)
  43. Permutations of Subsets of a Multiset
  44. A general solution for the probability of getting at least $k$ out of $n$ total distributed objects
  45. How many combinations of couples sitting on a roundtable?
  46. Given is a binary relation. Determine the Hasse diagram for it and two upper bounds

  47. Prove that no set of $n$ points can be triangulated in more than $2^{n \choose 2}$ ways.

  48. Why does raising this polynomial to a power, give the correct answer for a combinatorics problem?

  49. Maximum of minimum number of moves required for hardest 8 puzzle
  50. Find the number of arrangements that can be made of the letters of the word 'DIFFERENT' without changing the place of a vowel?

  51. Method for approaching combinatorial proofs
  52. Finding the numbers having a particular factor,an upper limit and a specific set of digits.

  53. Prove using mathematical induction

  54. Similar sequences of coin flips
  55. Prove that in a 10-element subset of $\{1, \dots , 50 \} $ there exist 2 $5$-element subsets such that the sums of all their elements are equal.
  56. Find the number of ways of arranging the letters

  57. Combinatorics: If my phone has a $5$-pin code to unlock it but I only remember $3$ digits, what are the outcomes?
  58. The number of ways in which 10 identical apples can be distributed to six children so that each child receives at least one apple
  59. The number of ways in which 5 different books can be given to 10 people with a condition

  60. Combinatorial proof for a Sterling identity

  61. Combinatorial Summation proof

  62. Proving using mathematical induction

  63. Permutation: Number of ways 4 cars could park

  64. Summation of combinations upto a specified bound

  65. Application of multinomial theorem in combinatorics

  66. How many ways are there to form a 16-digit number in which each digit appears at least once

  67. Combinatorics : Circular Permutation of N people with N-1 spots
  68. How many $10$ digit numbers containing $1$, $3$, $5$, $7$ and $9$ are there?

  69. Probability that m samples without replacement cover the entire set

  70. Countdown maths puzzle with a twist - ?multiset combinations with repetition?
  71. Combination from arbitrary number of type of items

  72. A power series = golden ratio = sin of arcsin formulae?!
  73. Number of vectors with the same $i$-th entry
  74. How does probability rate increase in this situation?

  75. What is the generating function for the number of Multisets

  76. Is this correct: Inflection points of Euler number graph in Island-Mainland transition correspond to spanning cluster site percolation threshold?

  77. Find $\sum_{n=1}^{10^6}\lfloor\sqrt n\rfloor$.
  78. Average vector norm after 'dropping' a few dimensions
  79. Zip Code Combinations
  80. In how many ways can you put two people in $5$ seats in a row if they cannot sit together?
  81. Question about the proof of the Mobius function for the lattice of subspaces
  82. What is the ratio of the number of ways to represent a number with a sum of $k$ numbers?

  83. A homework problem about set theory
  84. Formation of a 7 digit number using 3 digits with given condition

  85. How many permutations of 160 outputs from binomial B(1, p) if p varies?

  86. Phase 10 probabilities

  87. Calculating the probability of being dealt a straight in the Phase 10 card game

  88. Horse race combinations when ties are allowed

  89. Looking to get a handle on SSCG(3) (which is much, much larger than TREE(3))

  90. If I have a certain word, how can I find the lowest number of characters that must remain in their original spots if I permute it?

  91. Fibonacci and Lucas series technique

  92. Completely marked squares in squares

  93. Picking a sample of N numbered balls

  94. Is there some combinatorial intuition behind generating functions of sequences?
  95. Neighbor-difference permutations

  96. Combinations question - why is my approach wrong?

  97. Number of colourings for which the vertices of a square can be coloured by three different colours such that adjacent vertices get different colours.

  98. How many permutations avoid previous adjacencies?
  99. If $A$ is the alternating operator, prove that $A(A(\omega\otimes\eta)\otimes\nu)=A(\omega\otimes\eta\otimes\nu)$

  100. Calculating the Shapley value in a weighted voting game.