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标题: A GWD math, pls help me to solve. [打印本页]

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作者: tracyyahoo    时间: 2011-8-25 09:58
标题: A GWD math, pls help me to solve.
A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?

(A) 5
(B) 6
(C) 9
(D) 24
(E) 36

pls explain me why???? Thank you.

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作者: justgo    时间: 2011-8-25 10:09
六个人身高各不同，站成两排，后面三个前面三个。每排的人的身高必须从左到右依次增加，第二排的每个人必须比站在他前面的那个人要高。问有几种排法。
令1、2、3、4、5、6分别代表这六个人以及这六个人的身高。那么可以推断1只能排在前排最左边，6只能排在后排最右边。那么5就不能排在后排最左边以及前排中间，同时2不能排在后排中间以及前排最右边。然后分类排一下，共5种排法。

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作者: wyw1018    时间: 2011-8-25 10:09
设1，2，3，4，5，6为从低到高的6个人
根据题意1只能在第一排最左边，6只能在第二排最右边
2有两种排法，在第一排1的右边或者第二排1的边
5有两种排法，在第一排最右边6的前面或者第二排6的左边
因此共有5种排法：
123/456， 124/356，125/346，135/246，134/256

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