1. Priority method for special elements (or positions): The problem of arrangement and combination is nothing more than the relationship between "elements" and "positions", that is, where an element is arranged or what elements are arranged in a certain position. Therefore, for the restricted permutation and combination problem, the restriction of elements (or positions) can be given priority.
2, the adjacent problem "binding method" For the arrangement of adjacent elements, you can first "bind" adjacent elements to see an element (whole), first arrange with other elements, and then arrange between adjacent elements.
3. Non-adjacent problem "interpolation method": For the problem of non-adjacent elements, other elements can be arranged without considering constraints, and then the non-adjacent elements can be inserted into the gaps (including both ends) of the arranged elements.
4. Sorting problem "disorder method": For the problem of arranging elements in a certain order, you can first consider the arrangement of unordered elements and then divide it by the complete arrangement of several ordered elements.
5. Sorting problem "Direct Sorting": N elements are divided into m (m
6. Comprehensive problem solving: permutation and combination comprehensive problems are more complicated due to many restrictions. When solving this kind of problem, we should pay attention to the basic strategies and methods to solve the problem, grasp the essence of the problem and adopt appropriate methods to solve the problem.
7. Classification and step-by-step method: To solve the comprehensive problem of permutation and combination, we should follow the principle of "classification according to the nature of elements and step by step according to the development process of things", so that the classification standard is clear, the step-by-step level is clear, and the key points are not missed.
8. Exclusion method: For problems with negative words, the unqualified exclusion method can also be eliminated as a whole. Attention should be paid at this time, neither more nor less.
9. Diagram (table) method: For some comprehensive problems, if there is no solution for the time being, you can consider returning to textbooks and using tree diagram, block diagram or chart method to solve them.
10, at most, at least the indirect method of the problem: it is very troublesome to discuss the combination problem with "at most" and "at least", and the problem can be simplified if the indirect method is used.
1 1. Role transformation method: The problem of repeated arrangement and combination of elements can be solved by changing elements and positions.
What is permutation and combination:
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.
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, and various counting skills are produced.
At the same time, people have a profound understanding and research on numbers. In the process of the formation and development of various mathematical branches closely related to shapes, such as geometry, topology and category theory, the diversity of numbers and shapes is gradually discovered from the diversity of shapes, and various skills of numbers and shapes are produced. Modern set theory and mathematical logic reflect the potential combination of number and shape.