The arrangement A(n, m)=n×(n- 1). (n-m+ 1)=n/(n-m)(n is subscript and m is superscript, the same below).
Combination C(n, m)=P(n, m)/P(m, m) =n/m(n-m).
Extended data:
Modern set theory and mathematical logic reflect the potential combination of number and shape. However, modern algebraic topology and algebraic geometry closely link numbers with shapes. All these have had and will continue to have a far-reaching impact on the formation and development of modern combinatorics centered on digital skills.
From this point of view, combinatorics is closely related to other branches of mathematics. Some of its research contents and methods come from various branches and are also applied to various branches.
Of course, combinatorics, like other branches of mathematics, has its own unique research problems and methods, which stem from people's discovery and understanding of numbers, shapes and their relationships in the objective world.
For example, in the Book of Changes in ancient China, the period of 60 years was recorded by ten heavenly stems and twelve earthly branches, and the Rubik's Cube was recorded in the river map of Luoshu, which was the earliest combination problem and even architectural contextualism.
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