GWD 00-33

[eureka]

Q33:
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

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我是用土法煉鋼慢慢算的，請問各位有沒有其他的解法，謝謝!!!!!

[吳]

_________
6 a3 a4
_________
a1 a2 1
_________

6人身高:由1-6表示1最矮6最高,圖中最高跟最矮位置已經固定
a1-a4可以由2-5四個人來排
a2只可以排第2.3高,
a2的選擇->a1的選擇
2->3.4.5
3->4.5
a2,a1排完a3,a4的排法就只有一種了
所以總共是5種

好像有點亂,希望你看的懂~~