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Twelvefold way
In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical
Lottery mathematics
lottery game. It is based heavily on combinatorics, particularly the twelvefold way and combinations without replacement. In a typical 6/49 game, each player
Distribution
distributions of m objects to n recipients, subject to various conditions; see Twelvefold way Species distribution, the manner in which a species is spatially arranged
Order (mathematics)
in the Josephus permutation Ordered selections and partitions of the twelvefold way in combinatorics Ordered set, a bijection, cyclic order, or permutation
Discrete mathematics
on counting the number of certain combinatorial objects - e.g. the twelvefold way provides a unified framework for counting permutations, combinations
Stars and bars (combinatorics)
{\displaystyle \textstyle {7-1 \choose 3-1}=15} ways to distribute the coins. Twelvefold way Feller, William (1950). An Introduction to Probability Theory and Its
Ars Conjectandi
subject. It also addressed problems that today are classified in the twelvefold way and added to the subjects; consequently, it has been dubbed an important
Combinatorics
is the basic example of a problem in enumerative combinatorics. The twelvefold way provides a unified framework for counting permutations, combinations
Partition (number theory)
defined by partitions into consecutive integers Multiplicative partition Twelvefold way Ewens's sampling formula Faà di Bruno's formula Multipartition Newton's
Stirling numbers of the second kind
with n members Stirling numbers of the first kind Stirling polynomials Twelvefold way Partition related number triangles Ronald L. Graham, Donald E. Knuth