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标题: Gmat Prep-math [打印本页]

作者: cournot 时间: 2006-6-14 23:14
标题: Gmat Prep-math

AT a dinner party,5 people are to be seated around a circular table,two seating arrangements are considered different only when the position of the people are different relative to each other.what is hte total number of different possible seating arrangements for the group?

the answer is 24, but I figure out it's 120?

[此贴子已经被作者于2006-6-14 23:18:24编辑过]

作者: lovetiky 时间: 2006-6-15 09:14

P(5 5)=120, but this contain the redundance

如果我们只看着某一个座位，不管那个人坐，都会出现arrangement一样的情况。

换种说法，就是五个人已经排好了一圈，但是他们可以顺时针或者逆时针移位。

这样的排法是算在P(5 5)中的，但是在题目中只算一种

所以应该P(5 5)/5=24

作者: hitlzc 时间: 2006-6-15 09:21

因为two seating arrangements are considered different only when the position of the people are different relative to each other.

你算120是忽略了这个条件。

相对位置相同即认为是相同的。

应该是P（4，4）=24

这中圆形排列可参考

http://forum.chasedream.com/dispbbs.asp?BoardID=22&ID=3108&replyID=&skin=1

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