[中學] 排組
abcdefg共7人排成一列
則abcd中恰2人相鄰的排法？
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我的算法是
(1)4人中取2人相鄰：C(4,2)=6
(2)以ab相鄰為例
ab e f g
^ ^ ^
4! x 2! x [ C(3,1)x2! + C(3,2)x2! ] = 576
其中C(3,1)x2!是cd相鄰
C(3,2)x2!是cd不相鄰
6x576=3456
但答案應該是2592（我用反面算的）
請問我上面算式哪裏錯了？
又應該怎麼改？
謝謝
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※ 文章網址: https://www.ptt.cc/bbs/Math/M.1432827185.A.06D.html
※ 編輯: hungyastyle (49.218.83.233), 05/28/2015 23:36:40
→
05/28 23:36, , 1F
05/28 23:36, 1F
e f g
^ ^ ^ ^
4選3空隙插入口口 口 口
3! x C(4,3) x 4! = 576
我這樣算也錯@@
※ 編輯: hungyastyle (49.218.83.233), 05/28/2015 23:43:27
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05/28 23:47, , 2F
05/28 23:47, 2F
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05/28 23:52, , 3F
05/28 23:52, 3F
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05/29 00:00, , 4F
05/29 00:00, 4F
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05/29 00:00, , 5F
05/29 00:00, 5F
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05/29 00:02, , 6F
05/29 00:02, 6F
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05/29 00:04, , 7F
05/29 00:04, 7F
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05/29 00:05, , 8F
05/29 00:05, 8F
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05/29 00:07, , 9F
05/29 00:07, 9F
答案應該是2592沒錯吧(?)
我是用全部-不相鄰-3人相鄰-全相鄰
=5040-144-1728-576=2592算的
我算式只要改成
6 x 4! x 2! x [ C(3,1)x2! + C(3,2)x2!/2 ] = 2592 就對了
但蠻容易忽略那個除以2的ˊ_>ˋ
※ 編輯: hungyastyle (49.218.83.233), 05/29/2015 00:17:52
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05/29 00:11, , 10F
05/29 00:11, 10F
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05/29 00:19, , 11F
05/29 00:19, 11F
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05/29 00:19, , 12F
05/29 00:19, 12F
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05/29 00:21, , 13F
05/29 00:21, 13F
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05/29 00:21, , 14F
05/29 00:21, 14F
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05/29 00:24, , 15F
05/29 00:24, 15F
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05/29 00:26, , 16F
05/29 00:26, 16F
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05/29 00:29, , 17F
05/29 00:29, 17F
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05/29 01:33, , 18F
05/29 01:33, 18F
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