2022 Henan Provincial Examination Preparation: Don't be afraid, easily solve the problem of ring arrangement
Author: Henan Branch - Yang Yang Reviewer: Henan Branch - Zhao Kun
In the process of preparing for the test, most candidates think that the quantitative relationship is difficult, and even think that the quantitative relationship is the most difficult of all the modules of the test, and directly choose to give up in the exam. Especially the permutation combination in the quantitative relationship, when to use the permutation and when to use the combination, the use of addition or multiplication, more headaches, although the permutation and combination of related topics is more difficult, but each type of problem has its corresponding problem characteristics, and we also summarized the corresponding solution ideas. Next, I will explain to you a type of question type in the permutation combination -
Ring arrangement combination.
First of all, let's first understand what is a ring arrangement combination. The basic model of the ring arrangement is: "n people in a circle, ask: How many different methods are there?" ", the formula:
【Example 1】There are three children playing in a circle, how many different arrangements are there?
a.6 b.4
c.2 d.1
Answer: c
【Analysis】The first step, to identify the question type, there are n individuals in a circle, how many arrangements, and examine the ring arrangement combination;
The second step, to apply the formula, there are = 2 kinds, so choose c.
We need to note that this is not the same as standing in a row and arranging it before, so the result of the arrangement is not. In a circle, we look at the relative order of all the people, for example, if the three people are A, B, and C. As far as A is concerned, B sits on his left C sits on his right, and C sits on his left B sits on his right, which are two completely different situations, and there are only these two arrangements in total, as shown below.
In addition, whether we use B or C as the subject of study, or change the position clockwise and counterclockwise, it will be repeated. Therefore, it can be understood that no matter who is the object of study, first fix one of them (who is the same), and the rest of the people are fully arranged, so the three people are arranged in a circular arrangement, and there are a total of = 2 different arrangements. So if it's n individuals in a circle, there are different arrangements.
【Example 2】There are 9 children holding hands in a circle to play the game, asking how many different ways are there in total?
a.35280 b.40320
c.362880 d.456720
Answer: b
The second step, to apply the formula, there are = 40320 kinds, so choose b.
So, select the b option.
【Example 3】6 children in a circle to do a game, Xiaohua and Xiaoming need to be next to each other, ask how many ways to arrange?
a.360 b.240
c.120 d.48
Answer: d
【Analysis】In the first step, this question examines the permutation and combination problem, which belongs to the method and skill category.
The second step, xiaohua and Xiaoming are tied together, which is equivalent to a ring arrangement of 5 elements, Xiaohua and Xiaoming have an order, then the arrangement method has x2 = 48 (species).
So, select the d option.
Through the explanation of the above three questions, I believe that students have a basic understanding and understanding of the ring arrangement, and we will find that as long as we can identify the question type, it is not difficult to apply the formula. However, in the process of the actual examination, in order to increase the difficulty of the questions, many questions will be the same as Example 3, combined with other methods in the permutation combination to test the candidate's comprehensive ability, when encountering such questions, we should not be afraid of difficulties, only need to follow the corresponding solution methods of each type of question type.
Mind map
Yes
Kinds of possibilities
Original link: Huatu Education https://xinxiang.huatu.com/2021/0612/2139456.html