天山 09-33

[schung0529]

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

The answer is A...Why?

[vivid]

這題有沒有人有比較好的做法
因為我每次都用畫的
總之遵循左不能比右高 前不可比後高的原則
然後最高最矮的位子是固定的
期待有高手提供更好的解法

[zazer.lin]

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

The answer is A...Why?

題目大意是說:
有六個身高不同的人,要排上下兩排,每排三個人.
且排隊的順序是1.上排的身高要大於下排的身高 2.每一排的身高要由左至u右遞增

設六個人為A, B, C, D, E, F
且A < B < C < D < E < F

依據題意, 排隊要符合下列的情形

\$m[1]: \$m[1]


高 2 4 6

低 1 3 5
  低   高


由上圖可知, 1的位置一定是六人中最矮的, 6的位置一定是六人中最高的.
所以A就一定是在1的位置, 所以F就一定是在6的位置, 剩下的四個人排列組合.
因為只剩四個人, 且有一定的依存關係, 所以用排排看, 應該是不會花太多的時間.

<I>
B D F
A C E

<II>
C D F
A B E

<III>
B E F
A C D

<IV>
C E F
A B D

<V>
D E F
A B E

不好意思...小弟的能力有限...只會用土法煉鋼的方式...
如果有哪位大大有更為快速的方法...請不吝指教...感謝