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2. Stars and bars (combinatorics) - Wikipedia

   en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)

   It can be used to solve a variety of counting problems, such as how many ways there are to put n indistinguishable balls into k distinguishable bins. [4] The solution to this particular problem is given by the binomial coefficient ( n + k − 1 k − 1 ) {\displaystyle {\tbinom {n+k-1}{k-1}}} , which is the number of subsets of size k − 1 ...

3. Combinatorial optimization - Wikipedia

   en.wikipedia.org/wiki/Combinatorial_optimization

   A minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.

4. Combinatorics - Wikipedia

   en.wikipedia.org/wiki/Combinatorics

   Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures.It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.

5. Morphological analysis (problem-solving) - Wikipedia

   en.wikipedia.org/wiki/Morphological_analysis...

   Problems that involve many governing factors, where most of them cannot be expressed numerically can be well suited for morphological analysis. The conventional approach is to break a complex system into parts, isolate the parts (dropping the 'trivial' elements) whose contributions are critical to the output and solve the simplified system for ...

6. Combinatorial modelling - Wikipedia

   en.wikipedia.org/wiki/Combinatorial_modelling

   So, a partition problem can be solved by transforming it into a distribution one and applying the correspondent operation provided by the distribution model (previous table). Following this method, we will get the number of possible ways of dividing the set. The relation between these two models is described in the following table:

7. Combinatorial design - Wikipedia

   en.wikipedia.org/wiki/Combinatorial_design

   {1,2,3,4,7} {1,2,5,6,7} {3,4,5,6,7}. Lotto designs model any lottery that is run in the following way: Individuals purchase tickets consisting of k numbers chosen from a set of n numbers. At a certain point the sale of tickets is stopped and a set of p numbers is randomly selected from the n numbers. These are the winning numbers.