Permutations and combinations are a common and important type of questions in quantitative relationship questions.
When solving this type of problem, it is very helpful to understand the concept and application of misalignment rearrangement.
In this article, the concept and solution method of dislocation rearrangement will be introduced in detail, and analyzed through examples to help students better understand and master.
Misalignment and rearrangement refers to the situation where some elements are arranged according to certain rules, and some elements cannot appear in a specific position, but need to be rearranged in other positions. In permutations, dislocation and rearrangement are often related to constraints, and the correct answer can be obtained by analyzing and reasoning the problem.
The method of solving for misalignment rearrangement can be summarized as follows:
Determines the total number of elements and the number of non-placeable locations;
Count the number of places that can be placed;
The result of the misalignment rearrangement is calculated using the permutation combination formula.
Analysis: First, determine that the total number of elements is 3, and each student has 2 non-placeable positions (two seats next to them). Then the number of places that can be placed is 3-2=1. According to the method of dislocation rearrangement, the result is calculated using the permutation combination formula:
Result = Number of places that can be placed Total number of elements - 1)! = 1 × 3-1)! = 1 × 2! = 1 × 2 = 2Therefore, the three students have 2 different seating arrangements.
Resolution: The total number of elements is 5, and each player has 3 non-placeable positions (the middle position and the two positions next to it). The number of places that can be placed is 5-3=2. According to the method of dislocation rearrangement, the result is calculated using the permutation combination formula:
Result = Number of places that can be placed Total number of elements - 1)! = 2 × 5-1)! = 2 × 4! = 2 × 4 × 3 × 2 × 1 = 48As a result, the five players have 48 different stances.
Analysis: In this question, the restriction of at least one manager participating is taken into account. Therefore, when calculating the misalignment rearrangement, we can calculate it in two cases.
Scenario 1: Assignment of one manager and three employees.
Result 1 = Manager Assignment Employee Assignment = c(5, 1) c(8, 3) = 5 8 7 6) (3 2 1) = 560Scenario 2: Two managers and two employees are assigned.
Result 2 = Manager Assignment Employee Assignment = c(5, 2) c(8, 2) = (5 4) (2 1) 8 7) (2 1) = 280The final result is the sum of Outcome 1 and Outcome 2
Final Result = Outcome 1 + Outcome 2 = 560 + 280 = 840Therefore, there are 840 different ways to choose to send an inspection team.
This paper introduces in detail the application of dislocation rearrangement in the question type of the number relationship of public *** line test.
We can see that misalignment rearrangements work well when solving permutations with constraints. It is very important for candidates to grasp the concept of misalignment rearrangement and how to solve it.
It is hoped that this article can help students better understand and grasp the problem of dislocation and rearrangement in the question type of quantitative relationship.