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14 Sep 2003, 04:34
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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.
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.
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14 Sep 2003, 05:02
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i think answer is 7!.
I know this is counter intuitive, let me first begin with a simple example of permutation in a circle.
First if it is a circle with no marking on any position answer wud be = 6!
This is because for the first person all positioins are identical/same, so he has no choice. Thus choice begins with 2nd persona who has 6 choices, 3rd 5, 4th 4 ... and so on we get total ways to arrange them = 6!
Now when one position is marked then all positions in a circle becomes unique (because of red mark). Thus from the 1st person itself we will have choices. Hence answer = 7!
something more to ponder: if clockwise and anti-clockwise does't matter then answer = 7!/2 (In 7! we assume that clockwise and anticlock wise are different arrangements)
hope this helps...
-Vicks
I know this is counter intuitive, let me first begin with a simple example of permutation in a circle.
First if it is a circle with no marking on any position answer wud be = 6!
This is because for the first person all positioins are identical/same, so he has no choice. Thus choice begins with 2nd persona who has 6 choices, 3rd 5, 4th 4 ... and so on we get total ways to arrange them = 6!
Now when one position is marked then all positions in a circle becomes unique (because of red mark). Thus from the 1st person itself we will have choices. Hence answer = 7!
something more to ponder: if clockwise and anti-clockwise does't matter then answer = 7!/2 (In 7! we assume that clockwise and anticlock wise are different arrangements)
hope this helps...
-Vicks
15 Sep 2003, 23:45
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Vicky
i think answer is 7!.
I know this is counter intuitive, let me first begin with a simple example of permutation in a circle.
First if it is a circle with no marking on any position answer wud be = 6!
This is because for the first person all positioins are identical/same, so he has no choice. Thus choice begins with 2nd persona who has 6 choices, 3rd 5, 4th 4 ... and so on we get total ways to arrange them = 6!
Now when one position is marked then all positions in a circle becomes unique (because of red mark). Thus from the 1st person itself we will have choices. Hence answer = 7!
something more to ponder: if clockwise and anti-clockwise does't matter then answer = 7!/2 (In 7! we assume that clockwise and anticlock wise are different arrangements)
hope this helps...
-Vicks
I know this is counter intuitive, let me first begin with a simple example of permutation in a circle.
First if it is a circle with no marking on any position answer wud be = 6!
This is because for the first person all positioins are identical/same, so he has no choice. Thus choice begins with 2nd persona who has 6 choices, 3rd 5, 4th 4 ... and so on we get total ways to arrange them = 6!
Now when one position is marked then all positions in a circle becomes unique (because of red mark). Thus from the 1st person itself we will have choices. Hence answer = 7!
something more to ponder: if clockwise and anti-clockwise does't matter then answer = 7!/2 (In 7! we assume that clockwise and anticlock wise are different arrangements)
hope this helps...
-Vicks
I am not sure ,but Akamai told us something about a rotation factor...
Dont we have the rotation factor into account when arranging things in a Circle.
Akamai..can you help!
