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Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決
Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決 
高一排列組合。
Aug 1st 2013, 14:56

Yahoo!奇摩知識+有答案，詳情請看以下連結，我節錄你需要的情況如下：
http://tw.knowledge.yahoo.com/question/question?qid=1007111307989

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恰用 5 色: ( 先定位置 ~ 以長邊定位 )

( i ) 若 2 長邊同色:

2 長邊從 5 種顏色中選 1 種顏色 ~ C51 ＝ 5

剩餘的 4 面選 4 種顏色 ~ 亦即 4 異色

4! ＝ 24

把長邊定位後, 由於做 180o 旋轉, 都是屬於同一種情形, 也就是說旋轉數為 2

不同於 “恰用 4 色之 ( i ) 若 2 長邊同色” 的是 ~ 此部份雖同為 “若 2 長邊同色”,

但 4 面為 4 異色, 故需除以翻轉數 2

塗法有

5 * 24 / 2 / 2 ＝ 30

( ii ) 若兩長邊不同色:

2 長邊從 5 種顏色中選 2 種顏色 ~ C52 ＝ 10

剩餘的 4 面選 3 種顏色 ~ 亦即 2 同色 2 異色

3! * 2 ＝ 12 ( 理由同上 )

把長邊定位後, 由於做 180o 旋轉, 都是屬於同一種情形, 也就是說旋轉數為 2

塗法有

10 * 12 / 2 ＝ 60

故, 塗法共有

30 ＋ 60 ＝ 90


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參考資料： Yahoo!奇摩知識+

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