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## #1 2006-11-14 07:55:29

Neha
Member
Registered: 2006-10-11
Posts: 173

### how many

how many different ways can 5 objects be arranged in a circle????????

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## #2 2006-11-14 08:20:07

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

### Re: how many

By "5 objects"; Do you mean they have to be the same or they can be different?

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## #3 2006-11-14 08:25:00

Neha
Member
Registered: 2006-10-11
Posts: 173

### Re: how many

i dont know but that is how the problem was written....

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## #4 2006-11-14 09:17:17

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: how many

If they are the same, the answer 1 is, which is uninteresting.  Therefore, they are all different, QED.

So we have different objects.  On the first choice, we have 5, on the second 4, third 3, fourth 2, and fifth 1.  This leads us to the conclusions that there are 5! ways.

But wait!  That would mean:

1 3 2 5 4

and

4 1 3 2 5

Are different.  But they aren't!  Something is wrong.  We either have to change the way we count them, or we have to take into account these repeates.

Which would you like to do?  Either way you get a correct answer, but which is easier?  Which will take less time?  The choice is yours...

Think about it for a bit, and if you still need help, come on back and let us know.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #5 2006-11-14 11:08:20

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: how many

Expanding on what Ricky said, to get around the problem counting a rotated version of the same thing again, you need to make one of the objects always be in the same place. Then every version you make will be different, because the objects will always have different positions relative to the one that you fix.

If you don't want to count reflections twice either, then you'll need to divide the answer by 2.

Alternatively, you could say there aren't any ways of arranging 5 objects into a circle because you always make pentagons.

Why did the vector cross the road?
It wanted to be normal.

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