1. All permutation numbers of m(m≤n) elements taken out of n different elements are called permutation numbers of m elements taken out of n different elements, which are represented by symbol A(n, m).

2. Taking any m(m≤n) elements from n different elements and combining them into a group is called taking out the combination of m elements from n different elements; The number of all combinations of m(m≤n) elements from n different elements is called the number of combinations of m elements from n different elements. Represented by the symbol C(n, m).

Arrangement refers to taking out a specified number of elements from a given number of elements for sorting. Combination refers to taking out only a specified number of elements from a given number of elements, regardless of sorting.

The central problem of permutation and combination is to study the total number of possible situations in a given permutation and combination. Permutation and combination are closely related to classical probability theory.

Extended data

The development of permutation and combination:

According to the current research and development of combinatorics, it can be divided into the following five branches: classical combinatorics, combinatorial design, combinatorial order, graphs and hypergraphs, combinatorial polyhedron and optimization.

Since combinatorics involves almost all branches of mathematics, it may be as impossible to establish a unified theory as mathematics itself.

However, how to establish some unified theories on the basis of the above five branches or form some new branches of mathematics independently from combinatorics will be a new challenge for mathematicians in the 2 1 century.

References:

Baidu encyclopedia-permutation and combination