新书学酷字22th~~~

melindalmy

圆盘钥匙题~
小狼童鞋说了 圆形要除以N~~~~但是为什么捏？……
还有 有童鞋说——圆形排序是公式2/（n-1） 直接代入就行~~~~代入后跟小狼的答案是一样哒 但是又是为什么捏……
求助于走过路过的战友们~thx^^

------啊 我在CD发的处女主题~~~

sdcar2010

If n different people are sitting around a table, the possibility of 2 persons sitting next to each other is 2/(n-1).

1) Total possible arrangements of n people on a table = n! / n = (n-1)!
2) Total possible arrangements of n-1 people (assuming those two sitting together would be treated as a single person) = 2* (n-1)! / (n-1) = 2* (n-2)!  There is a 2 in the equation because the two persons are not identical.

The possibility of 2 persons sitting next to each other = 2* (n-2)! / (n-1)! = 2/(n-1)

sdcar2010

Total possible arrangements of n people on a table = n! / n = (n-1)!

The reason to devide n! by n is that when your connect the head to tail of a linear arrangement to form a circular arrangement, you will find that for each circular arrangement, you have n different possible linear arrangements because you can cut the ring formed at n different places to get a different linear arrangement!

melindalmy

If n different people are sitting around a table, the possibility of 2 persons sitting next to each other is 2/(n-1).

1) Total possible arrangements of n people on a table = n! / n = (n-1)!
2) Total possible arrangements of n-1 people (assuming those two sitting together would be treated as a single person) = 2* (n-1)! / (n-1) = 2* (n-2)!  There is a 2 in the equation because the two persons are not identical.

The possibility of 2 persons sitting next to each other = 2* (n-2)! / (n-1)! = 2/(n-1)

-- by 会员 sdcar2010 (2010/12/26 23:21:42)

灰常灰常感谢~~
但是我依然不能理解的是：
第一步 1）中为什么分母要除以n.......
貌似这是个基本知识。。。但一时半会儿实在是记不起为啥来了。。囧

sdcar2010

Linear: ABC, BCA, CAB
circular: Only -ABC-

melindalmy

Linear: ABC, BCA, CAB
circular: Only -ABC-

-- by 会员 sdcar2010 (2010/12/26 23:34:32)

额果断纠结了。。。
LINEAR的话 不是应该有 ABC,ACB,BAC,BCA,CAB,CBA 一共A33=六种咩

sdcar2010

Linear: ACB, CBA, BAC
circular: Only -ACB-

This and the above examples demonstrate that for one circular arrangement of n things, you have n linear arrangement of n things.

The reason to devide n! by n is that when your connect the head to tail of a linear arrangement to form a circular arrangement, you will find that for each circular arrangement, you have n different possible linear arrangements because you can cut the ring formed at n different places to get a different linear arrangement!

rinelylove

凡是遇到了钥匙链的，我们都默认一个规律：少算一个元素。就对了！

melindalmy

Linear: ACB, CBA, BAC
circular: Only -ACB-

This and the above examples demonstrate that for one circular arrangement of n things, you have n linear arrangement of n things.

The reason to devide n! by n is that when your connect the head to tail of a linear arrangement to form a circular arrangement, you will find that for each circular arrangement, you have n different possible linear arrangements because you can cut the ring formed at n different places to get a different linear arrangement!

-- by 会员 sdcar2010 (2010/12/26 23:51:31)

哈！我明白啦~~~~就是
圆变直线要乘以N
直线变圆要乘以1/N
啦~~~谢谢你！ 真是给我解释的好费力气~~~不过这下终于砂锅到底嘞~~嘿嘿
GOOOOOOD LUUUUUUCK FOR U!!!!!!!SINCERELY~

melindalmy

凡是遇到了钥匙链的，我们都默认一个规律：少算一个元素。就对了！

-- by 会员 rinelylove (2010/12/26 23:52:06)

嗯呢 升级版的 好记！
美女是快考试了么？ 加油+好运气！！！