[求助]GWD MATH 03- 20

stuchrischan · 发表于 2010-7-31 15:34:23

33、
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

Answer: A

393075583 · 发表于 2010-7-31 16:55:08

123
456

124
356

125
346

134
256

135
246

要是用算的也可以
因为要按高度排列，所以只要选定了元素就可以，不用考虑每个元素的位置。
刨除123这种情况
456
23不能同时出现在第二排
45不能同时出现在第一排
从23里选一个在第二排
从45里选一个在第一排即可
一共有4种选法
加上之前123 一共五种
456

stuchrischan · 发表于 2010-7-31 19:36:28

懂了，谢谢老兄！

andreasyang · 发表于 2010-8-1 03:17:45

这种只能穷举法了
一排第一个最矮，二排最后一个最高
6个人按123456排
还是比较快的

[求助]GWD MATH 03- 20

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