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排列组合应用题逻辑性强,又较抽象,思维形式独特,学生解题时往往无从下手。本文介绍配对法解排列组合问题,试图使学生在解题时增加一种有价值的思考方法。例1 n名选手参加乒乓球比赛,需要打多少场才能产生冠军? 比赛规则是:要淘汰1名选手必须进行1场比赛;反之,每进行1场比赛则淘汰1名选手。解:把被淘汰的选手与他被淘汰的那场比赛配对。因此,比赛的场次与被淘汰的人数相等,要产生冠军必须淘汰(n-1)名选手,故应进行(n-1)场比赛。这个问题就是利用配对法来解决的,比用
Arrangements and combinations of applications are logical, abstract, and unique in their thinking. When students solve problems, they are often unable to start. This article describes the pairing method to solve the problem of arranging and combining, trying to make students add a valuable way of thinking when solving problems. Example 1 For n players to participate in table tennis competitions, how many fields need to be played in order to win the championship? The rules of the game are: To defeat one player, one game must be played; otherwise, one player is eliminated for every one game. Solution: Pair the eliminated player with the match he was eliminated. Therefore, the number of matches in the game is equal to the number of eliminated players. To win the championship, (n-1) players must be eliminated. Therefore, (n-1) games should be played. This problem is solved using the pairing method.