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Re: One circular stage....there are seven positions in it, one [#permalink]
praetorian123 wrote:
One circular stage....there are seven positions in it, one of them is
marked by red color and one of seven people will stand on these
positions, how many arrangements are possible?

Is it 6! / 7 ?

please explain your answer.


Vicky is correct. By marking one of the position, you eliminate the rotational symmetry of the problem, hence, the answer is simply 7!

Another way of looking at it is:

There are 7 possible people that can stand on the red spot. For each one of those, we can arrange the other 6 in 6! different ways. Hence, there are 7 x 6! = 7! ways.

Clockwise and counterwise certainly do matter -- the same way left-to-right and right-to-left would in a row. HOWEVER, if we were talking about something we could pick up and flip over, say, a bracelet or hula hoop, they we would have "mirror image" symmetry and the answer would be 7!/2.
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Re: One circular stage....there are seven positions in it, one [#permalink]
praetorian123 wrote:
One circular stage....there are seven positions in it, one of them is
marked by red color and one of seven people will stand on these
positions, how many arrangements are possible?

Is it 6! / 7 ?

please explain your answer.


As far as I understood the initial verbiage, ONE out of seven people will stand on the positions. ONE means 1, the only.
We have to take one out of seven and arrange him on the stage.
7*7=49, no?
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Re: One circular stage....there are seven positions in it, one [#permalink]
stolyar wrote:
praetorian123 wrote:
One circular stage....there are seven positions in it, one of them is
marked by red color and one of seven people will stand on these
positions, how many arrangements are possible?

Is it 6! / 7 ?

please explain your answer.


As far as I understood the initial verbiage, ONE out of seven people will stand on the positions. ONE means 1, the only.
We have to take one out of seven and arrange him on the stage.
7*7=49, no?


There are 7 ways to pick the person to be put on the red spot and 6! ways to put the remaining 6 people. So, the answer would be 7 * 6! = 7! if direction does not matter and 7!/2 if it does.
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Re: One circular stage....there are seven positions in it, one [#permalink]
With the red mark, one position gets fixed where 7 persons can be arranged in 7 ways.
For rest of the 6 places,distinct items can be arranged in 6! ways. looks perfect.

[/code]
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Re: One circular stage....there are seven positions in it, one [#permalink]
I understand this solution, believe me. There is absolutely no need to post it twice. But this solution is OK for the following verbiage: One circular stage....there are seven positions in it, one of them is
marked by red color and seven people will stand on these
positions, how many arrangements are possible?

see a difference?



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