GWD-1中的一题数学排列组合题,,谢谢指点....

lydiahst

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

OA:A

lydiahst

怎么都没人帮忙回答下啊???

napoleon7424

这个题我也做错了~因为忽略了一个条件。
我是这么想的，简化题目要求即两个，一要求每排从左到右顺序从小到大排列，二每一列后排比前排高。
由于这道题目人数比较少，所以可以简单寻找，假设六个人身高从小到大一次为123456
简单分析，一排左一一定为1，123中至少两个在第一排，456至少两个在第二排。
在这种情况下，一排左二可以且只能为2或3
一排左二为2时，有：123/456,124/356,125/346三种
一排左二为3时，有：134/256,135/246二种
一共五种。

fanlion

可以这样想，首先1只能前排最左，6只能后排最右，然后4和5只能后排中间和前排最右，然后分两种情况，就是4和5对调的排列，2+3种