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题库 / GMATLA-PS-14
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?
5
6
9
24
36
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①每排从左到右依次增高
②第二排比第一排都高
设：1，2，3，4，5，6
则：
①1，2，3；4，5，6
②1，2，4；3，5，6
③1，2，5；3，4，6
④1，3，4；2，5，6
⑤1，3，5；2，4，6
下排中位只能为2/3：
当2时，下排第三位可以是3、4、5，C（1，3）=3，剩下两个数字位置随即确定
当3时，上排第三位只能是4，5，C（1，2）=2，剩下两个数字位置随即确定
所以结果3+2=5
123,124,125,134,135