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Trees planted around a circle

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by mlaboda » Sat Sep 05, 2009 8:17 pm
In how many different arrangements can six trees be planted on the circumference of a circular garden if two arrangements are considered different when the positions of the trees are different relative to those of the others?
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by Nermal » Sun Sep 06, 2009 2:05 am
I think it's 6!/6 = 120
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by mlaboda » Sun Sep 06, 2009 7:55 am
Thanks for the response. Why did you divide by 6?
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by tom4lax » Sun Sep 06, 2009 10:59 am
Same answer, different approach.

You can place the first one anywhere, so 1. Then place the other 5 in 5!. So answer is 5! = 120
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by Nermal » Sun Sep 06, 2009 10:59 pm
As tom4lax said it doesn't matter where you start.

It is stated in the question:
if two arrangements are considered different when the positions of the trees are different relative to those of the others?

There are always 6 possibilities where you can start from and they are all considered to be equal.

HTH
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