The essential difference between C (combination) and A (arrangement) lies in whether the extracted elements are ordered or not. A is the so-called arrangement, that is, a specified number of elements are taken out from a given number of elements for sorting. C is a combination, which means that only a specified number of elements are taken out of a given number of elements regardless of the sorting.

For example, choose 5 letters from 26 letters.

Arrangement: A (A(26,5) means to arrange five letters in a line from 26 letters; That is, ABCDE is different from brominated diphenyl ethers and brominated diphenyl ethers.

Combination: C(26, 5) means that there is no order in choosing five of the 26 letters; In other words, ABCDE is equivalent to ACBDE and ADBCE.

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.