一道GWD，求帮忙！

Roselle

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
答案是5。

Rebeca

Suppose these six people are A B C D E F G, and their heights are ascending from A to G

The arrangements are:

2L 2M 2R
1L 1M 1R

A can only be in 1L and G could only be in 2R. B could be in either 2L or 1M.  

So let's put B at 2L first. In this case, C has to be in 1M:
B D F           B E F
A C E           A C D

Now let's try to put B at 1M. Then 1R could be either C, D or E.
D E F         C D F      C E F
A B C         A B E       A B D

-- by 会员 sdcar2010 (2011/1/10 10:24:40)

你的数学思维一直都这么强大~~~
我基本上也算得上是你粉丝了~~~哈哈

sheilabravo

暴力穷举

Roselle

可否有其他方法？如果人多的话不好这么排啊。

sdcar2010

Suppose these six people are A B C D E F, and their heights are ascending from A to F

The arrangements are:

2L 2M 2R
1L 1M 1R

A can only be in 1L and F could only be in 2R. B could be in either 2L or 1M.  

So let's put B at 2L first. In this case, C has to be in 1M:
B D F           B E F
A C E           A C D

Now let's try to put B at 1M. Then 1R could be either C, D or E.
D E F         C D F      C E F
A B C         A B E       A B D