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          “插空法”速解排列組合-2020年國家公務員考試行測解題技巧

          http://www.9999gx.com       2019-07-19 15:57      來源:公考通
          【字體: 】              

            在行測數量關系中,排列組合問題算是考生最頭疼的問題了,考生往往需要思考很長時間,卻依舊做不出來,導致考生在做題過程中會直接跳過排列組合問題,這無疑會影響考生的最終得分。其實在排列組合中有一部分特殊題型,能夠達到快速解題的效果,今天公考通帶大家一起來看一下排列組合中的常用方法——插空法。


            例1.有A、B、C、D、E五個人要排成一行,A、B要求不相鄰,問一共有多少種排列方法?


            A.24   B. 36   C.48   D.72


            【答案】D。解析:問一共有多少種排列方法,從問題可以看出是排列組合問題,因為存在排序,交換A、B、C、D、E五個人的位置會對結果造成影響,所以是排列。但這個問題中有一個要求:“A、B要求不相鄰”,則可以先排C、D、E,為A33;之后在C、D、E形成的四個空中選兩個空插入A、B,為C42,也就滿足了題干要求的“A、B要求不相鄰”;但此時A、B交換順序對結果有影響,應考慮A、B的順序,為A42;所以列式為A3x A42=6x6x2=72,選擇D。


            提醒:排列組合問題中,出現要求“不相鄰”,可以用插空法進行快速解題。解題步驟為①先考慮其他元素②選空③排空。


            例2.五本不同的童話書和四本相同的漫畫書整齊的擺放在書架上,現在要求所有漫畫書不能擺放在一起,問有多少種擺放方法?


            A.120   B.1200   C.1800   D.17280


            【答案】C。解析:問有多少種擺放方法,屬于排列組合問題,出現“不相鄰”。考慮用插空法,步驟1先考慮剩余元素。五本不同的童話書沒有要求,先將童話書進行全排列,為A55。2選空,從五本漫畫書形成的六個空中選擇四個空房漫畫書,為C64。3排空,四本漫畫書相同,交換漫畫書的位置對結果無影響,因此可列式為A55 x C64 =120x15=1800,選擇C。


            提醒:插空法中第三步為排空,一定要注意交換元素順序對結果是否有影響。


            通過以上講解可以發現,排列組合問題中也有能夠快速解決的問題,學會這些問題能夠提高我們的能力與成績。

           

            學完理論知識后,想刷題提升可以下載公考通APP在線刷題。

           

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