Question 481474
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pls help me solve this problem in probability... thank you..


a ring of keys can hold 7 keys. In how many ways can the keys be arranged if the ring can be turned over?
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        The solution and the reasoning in the post by @Theo are incorrect.


        I came to bring a correct solution.



<pre>
The keys are on the ring - it means that we consider circular permutations of 7 keys.

There are (7-1)! = 6! = 720 circular permutations of 7 keys.



Next, the ring can be turned over.  It means that we identify arrangements
that differ by the mirror reflection.


So, we should divide 6! = 720 by 2.


The final <U>ANSWER</U> is: the number of all distinguishable arrangements is 720/2 = 360.
</pre>

Solved correctly.


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<H3>The post-solution note</H3>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This problem is not from probability, &nbsp;as you mistakenly write in your post.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The area of &nbsp;Math, &nbsp;to which this problem does relate, &nbsp;is called &nbsp;Combinatorics.