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2020年國考行測數量關系“插空法”速解排列組合

公考資料網 2019/08/12 11:33:17

  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,今天公考資料網(http://www.btdfsx.com/)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A33  x 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必勝公考APP在線刷題。


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