Gmat 排列组合题At a dinner party 5 people are to be seated around

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Gmat 排列组合题
At a dinner party 5 people are to be seated around a circular table.Two seating arrangments are considered different only when the positions of the people are different relative to each other.有多少种不用的arrangement
我不太明白什么叫做相对位置 .别光给个式子哦

就是说12345和34512是相同的,因为每个人的两边的人都完全一样,换句话说就是5个人坐好之后围着桌子转圈是相同的arrangement.
答案是
5!/5
第一个人有5个位子可以选择,第二个人有4个位子可以选,依次类推,于是一共有5!种坐法,但是因为转圈导致有5种坐法被认为相同,所以要除以5,于是最后答案就是24.
补充：
上面的算术一开始弄错了,应该是24,而不是12.
因为每1种排法都有其他4种排法和它是重复的,比如12345/23451/34512/45123/51234,因为是围着圆桌子,所以每个人在其中1种排法中左边的人都和其他4种相同,右边的人也是,所以要处以5.
此外,换一个思路也能解决这个问题：
第一个人虽然看上去貌似可以选5个座位,但是因为判断坐法是否相同的依据是相对其他人的位置,而不是坐在哪个座位上,所以实际上他选任何一个座位都没有区别,所以第一个人可以认为只有1个选择.由于第一个人已经坐下了,所以第二个人相对于第一个人的位置有4个选择.依次类推,最终答案就是1*4*3*2*1=24

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