Learn this chapter and get familiar with the basic things.

First of all, we must understand the concept of permutation and combination. The number of all different permutations (combinations) of m elements from n different elements is called the permutation number (combination number) of m elements from n different elements, where (n) m).

And skillfully use the principle of addition principle and multiplication to give priority to the special position of special elements. Common methods are: element analysis and position analysis. When there are few elements, enumeration method can be used (with the help of tree diagram), as well as adjacent problem binding method, interphase problem interpolation method, grouping method of the same element, sorting, and even grouping problem division (usually there are some relative relationships, such as height and size, etc. ) Sorting problem can also directly take out the sorted elements without arranging them, arrange the remaining elements in a straight row, and arrange the comprehensive problems first (classify the selected elements first when combining, and exclude them indirectly by direct classification (if it is difficult, it will be reversed), and arrange them in a special way, such as circular arrangement. ).

Two. detail

(1) Distinguish permutation and combination (the key is order or disorder)

(2) No matter whether the selected elements are the same, different or in between, the arrangement containing the same elements can be regarded as an ordered arrangement, which may sometimes involve repeated arrangement.

(3) Whether the grouping is uniform or uneven, and whether the master after grouping is determined. Generally, it can be divided into two parts, which are grouped first and then distributed.

3. Important mathematical thinking methods

(1) classification discussion (key and difficult points) (2) reduction (for example, when determining the number of lines in different planes, it is converted into determining the number of triangular pyramids) Learn to establish a basic model. Most problems can be transformed into basic models to deal with, and some new problems are mostly introduced after putting on vests for those common problems.

In addition, learning to cultivate the ability to solve more than one problem is not only conducive to developing intelligence, but also can verify the answer from another aspect when checking.

5. All the above are the mastery of theoretical knowledge. If you want to use it flexibly, you can't avoid doing more exercises.

All right, class, come on.

The permutation and combination in high school teaching is an elective course in liberal arts and a compulsory course in science, and there are also several permutations and combinations in universities. I suggest that the arrangement and combination should be based on video teaching.

I think it is important to understand the principle of permutation and combination. Although the two basic principles of "classified addition" and "step-by-step multiplication" are easy to say, basically a little more complicated permutation and combination problems are involved. Sometimes in the topic, many people don't know whether to add or multiply.

In addition, we must thoroughly understand the difference between "arrangement" and "combination". In short, whether it is related to the sequence or not, it is necessary to think clearly whether each step of calculation is "pumping" or "arranging". Take the simplest example: five people draw three, which is C5 3. This process is just drawing. Five people do three things with three, which is A5 3. This process includes not only drawing but also arranging music. Finally, some commonly used methods and the scope of application of each method are summarized, such as division method and opposite event method.

Finally, I want to make a suggestion. In order to better understand the concept of permutation and combination, it is suggested to replace combination with permutation directly. For example, I just gave an example: five people do three things with three, and A5 3 can be used directly without C5 3A3 3.

Of course, when learning mathematics, you still need to think more. If you do something wrong, you should analyze and think according to the answer. What's wrong with this question? Why is there a problem? And most importantly, think more about "how should I do this?" Why not use other methods? "I think we can really learn to understand this question, because sometimes we will encounter some questions that we don't know, and the answer may be easy to understand, but the hard part is," How did we think of doing this? "So if you really want to learn math well, you must know what it is and why.

(1) Abstracting several concrete mathematical models from various practical problems requires strong abstract thinking ability;

(2) The restrictive conditions are sometimes obscure, which requires us to accurately understand the key words in the question (especially logical related words and quantifiers);

(3) The calculation method is simple and has little connection with the old knowledge, but it needs a lot of thinking when choosing the correct and reasonable calculation scheme;

(4) Whether the calculation scheme is correct can't be tested by intuitive methods, which requires us to understand the concepts and principles and have strong analytical ability.

Keep in mind those commonly used formulas. Ask you casually, and you can immediately react the formula in your mind. This is the basic requirement. Secondly, you should be able to understand the essence of some abnormal formulas at a glance. Then, you need to know clearly what an arrangement is and what a combination is. This requires you to know whether it has anything to do with order. What has nothing to do with combination is arrangement. This is the first step to solve the problem. Whether a topic is an arrangement problem, a combination problem, or both, this is the first thing you need to make clear after you see the topic. Knowing this, you won't be contrary to the answer point when you answer the question. Finally, you need to answer in the form of a table. In this process, you need to know which information in the topic is useful and which is confusing.

The binomial theorem is to recite the formulas and then have a "holistic view", that is, some formulas are very complicated, but if you can take those complicated formulas as a whole, you will find that they are so simple, and then you can solve the problem well. Sometimes, if you don't have the conditions to use a formula, you have to find a way to replace it equivalently, such as multiplying a number and dividing it by a number, and so on.

I don't know if it's useful for you. You can try it. The most important thing is to remember the formula, then read more examples and do more exercises related to the examples. In this way, you will learn permutation and combination and binomial theorem well. Because mathematics is a process of "enlightenment and practice",

When I teach students, I ask them to divide the topic of probability into numerator and denominator, and then use multiplication, that is, permutation and combination, to find out the numerator and denominator respectively.

You must avoid enumeration when solving problems. It can't help you improve any understanding of probability, and is usually used when checking or the topic is incomprehensible. Firstly, the problem is divided into three parts: grasping (closing) at one time, not putting it back (sorting) in turn, and putting it back (to the power) in turn to solve it. Then translate the topic into mathematical language to determine how to multiply the numerator and denominator. It should be noted that the first order and the second order are synchronous in numerator and denominator.

There are two other situations, namely 1, which can only be counted, so it is a number. This kind of problem usually occurs when you are given an area in which there are a series of points that meet the conditions. The coordinates of points are generally integers, so there is nothing to say. Small area, violent enumeration; 2. Another question type is neither permutation nor combination, nor power, and it is difficult to enumerate. It considers the definition of classical probability, that is, the denominator represents the number of all feasible solutions, and the numerator represents the number of all feasible solutions that meet the conditions (such is the case in living languages).

For example, a takes an integer in 1-7, b takes an integer in1-kloc-0/3, and the probability that A+B sum is even, first determine the denominator, 7* 13=9 1, and then determine the numerator. The sum of two numbers is even, either the same or the same. So the final probability is 46/9 1.

Write more compositions. Words are the largest permutation and combination. The core point of my Storytelling Composition is that a story is a combination of three or more plots. You will find that you can learn Chinese well and math well, haha. For example, "I eat meat", "I like to eat meat" and "I am fat". In three sentences, how many stories can you tell? Four sentences, five sentences ... 100 sentences? Learn math, you can learn it in stories, and the situation is very important!

To learn permutation and combination well, we must first learn to distinguish whether to do something step by step or classified, step by step multiplication and classified addition. When discussing each step or category, we should pay attention to whether to consider the order, that is, whether the order has any influence on the final result, and then decide whether to arrange or combine. In short, we should learn to discuss in groups.

1. First understand the basic concepts of permutation and combination, how they come into being and what problems to solve.

2. Don't memorize formulas and basic theorems. If you can deduce the best, use a practical example to understand memory.

3. Do more exercises, practice makes perfect.

A 123 ... Use the exhaustive method to make statistics, and use B to summarize the regular arrangement.