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John draws a regular five pointed star in the sand, and at each of the 5 outward-pointing points and 5 inward-pointing points he places one of ten different sea shells. How many ways can he place the shells, if reflections and rotations of an arrangement are considered equivalent?

 
 Jan 24, 2023
 #1
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The number of arrangements is 10!/(5!*5!) = 252.

 
 Jan 24, 2023
 #2
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I am not too sure about the reflections part of it. 

 

First place a shell  down anywhere, call it A, now there are 9 shells left  so

9! takes into consideration of the rotation part

 

Maybe for the reflection you just divide by 2 becasue there is only one axis of symmetry through A

 

So maybe the answer is 9!/2

 

If you have access to the answers can you check and comment on whether this is the same.?

 
 Jan 24, 2023
edited by Melody  Jan 24, 2023
edited by Melody  Jan 24, 2023

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