I. Definition:
Permutation and combination is the most basic concept of combinatorics. The so-called 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.
The definition of permutation is that any M different elements are arranged in a column from N different elements in a certain order, which is called taking out an permutation of M elements from N different elements, and taking out the number of all permutations of M elements from N different elements, which is called taking out the permutation number of M elements from N different elements.
Second, the principle and application of permutation basic counting:
1, addition principle sum classification counting method
Each method in each category can accomplish this task independently. The specific methods in two different categories are different, that is, the classification is not heavy, and any method to complete this task belongs to a certain category (that is, the classification is not leaking).
2. Multiplication principle and step counting method
One method of any step can't complete this task, and this task can only be completed by continuously completing these n steps, and the counting of each step is independent of each other. As long as the methods used in a step are different, the corresponding methods to complete it are also different.
Three development processes:
Although mathematics began in ancient times, there was no skill because the development of social production level was still in the low stage. With people's understanding and research on numbers, in the process of forming mathematical branches closely related to numbers, such as the formation and development of number theory, algebra, function theory and even functional, the diversity of numbers is gradually discovered from the diversity of numbers.
People have a profound understanding and research on numbers. In the process of forming various mathematical branches closely related to shapes, such as the formation and development of geometric topology and category theory, the diversity of numbers and shapes has been gradually discovered from the diversity of shapes, and various skills of numbers and shapes have been produced. Modern set theory and mathematical logic embody the potential combination of number and shape.