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#1 2006-11-14 16:39:47

Loser_Virus
Member
Registered: 2006-11-14
Posts: 1

How many different ways?

There are eight horses.
There is one harness.
The harness can only be arranged one way.
There can only be two horses on each row.
There are four rows.
How many different ways can the horses be arranged?
Diagram:
1 2
3 4
5 6
7 8
Can you solve it any other ways besides the diagram?
If so, how?
Thanks in advance.
:]
Btw, First post.
<3JJ.

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#2 2006-11-17 05:51:22

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: How many different ways?

Reduce problem down to 2 horses, so then 2 1  or 1 2.

For 3 horses.  21 or 12 gets swapped with 3 on left or right, which makes 4 ways plus put 3 in the middle, so 6 ways.

For 4 horses 321 mix gets swapped with 4 on left or right which makes 12 ways, plus 4 in the two middle locations, so just keep thinking about it and write down stuff and you'll make progress understanding
perhaps how to get to the factorial answer, I think.

If you can't derive the factorial answer, don't feel bad, most people just memorize it.


igloo myrtilles fourmis

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