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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 ...
In statistics, the multiple comparisons, multiplicity or multiple testing problem occurs when one considers a set of statistical inferences simultaneously [1] or estimates a subset of parameters selected based on the observed values. [2] The larger the number of inferences made, the more likely erroneous inferences become.
Combinatorial modelling is the process which lets us identify a suitable mathematical model to reformulate a problem. These combinatorial models will provide, through the combinatorics theory, the operations needed to solve the problem.
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.
A solution to Kirkman's schoolgirl problem with vertices denoting girls and colours denoting days of the week [1] Kirkman's schoolgirl problem is a problem in combinatorics proposed by Thomas Penyngton Kirkman in 1850 as Query VI in The Lady's and Gentleman's Diary (pg.48). The problem states:
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.
Under Fisher's method, two small p-values P 1 and P 2 combine to form a smaller p-value.The darkest boundary defines the region where the meta-analysis p-value is below 0.05.. For example, if both p-values are around 0.10, or if one is around 0.04 and one is around 0.25, the meta-analysis p-value is around 0
Combinatorial explosion is sometimes used to justify the intractability of certain problems. [ 1 ] [ 2 ] Examples of such problems include certain mathematical functions , the analysis of some puzzles and games, and some pathological examples which can be modelled as the Ackermann function .