[問題]Prep-T1-Q77 PS

[gozui[origen]]

At a dinner party, 5 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?

(A) 5
(B) 10
(C) 24
(D) 32
(E) 120



Ans: (C)

請問藍字的地方是不是說, ABCDE 跟 BCDEA 是一樣的意思, 因為坐成一個圈圈時, 順序都一樣
如果是這樣的話, 那要如何求出有幾種組合呢?

[evangelinewu]

At a dinner party, 5 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?

(A) 5
(B) 10
(C) 24
(D) 32
(E) 120



Ans: (C)

請問藍字的地方是不是說, ABCDE 跟 BCDEA 是一樣的意思, 因為坐成一個圈圈時, 順序都一樣
如果是這樣的話, 那要如何求出有幾種組合呢?

沒錯～round table的排列看的是相鄰兩個人的順序...所以ABCDE 跟 BCDEA 是一樣滴

這種題型我的思考方式是...固定其中任何一人...讓剩下的人去排序
所以就是(N-1)階....
故本題4!=24

如果要想的更複雜一點
事實上五個人排圈圈...
ABCDE
BCDEA
CDEAB
DEABC
EABCD
等於是同一種...
故五個人排列原本有5!種排法(直線時）
故排圈圈時就是5!/5=4!
除以五是為了消除每次相鄰位置改變時都會有四種重複的情況

[gozui[origen]]

喔.... 我了解了
evangelinewu說明的好詳細喔
謝謝你