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排列问题是排列组合内容中的最基本的内容,由于涉及知识面广,条件复杂多样,解法灵活多变,很多同学解答排列问题时容易出错。下面通过一道例题给大家介绍解答排列问题的基本方法。例题(2013年全国大纲卷)6个人排成一行,其中甲、乙两人不相邻的不同排法共有___种(用数字作答)。解法1(插空法)先排其他4人,有A_4~4=24种方法;再将甲、乙二人插空,有A_5~2=20种方法。所以共有A_4~4·A_5~2=480种不同的排法。
Arrangement is the arrangement of the most basic content of the combination of content, due to the wide range of knowledge involved, the conditions are diverse and diverse, flexible solution, many students answer to the arrangement error prone. Below by a case to introduce the basic solution to the problem of arrangement. Examples (2013 National Outline Vol.) Six individuals are grouped together. Among them, there are a total of ___ (in figures) of different rankings in which non-adjacent persons A and B are located. Solution 1 (insert method) the first four other people, there are A_4 ~ 4 = 24 kinds of methods; then A, B two people inserted empty, there are A_5 ~ 2 = 20 kinds of methods. So a total of A_4 ~ 4 · A_5 ~ 2 = 480 different row method.