(New page: OK, so we need to put 5 indistinguishable objects into 3 indistinguishable boxes. The easiest way to do this is to just list the different possibilities. box box box 5 0 ...)
 
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The easiest way to do this is to just list the different possibilities.
 
The easiest way to do this is to just list the different possibilities.
  
box  box  box
+
 
 
   5        0        0
 
   5        0        0
 
   4        1        0
 
   4        1        0
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Notice that I did not label the boxes, this is because they are indistinguishable.  This makes it so I do not have to list 5-0-0, 0-5-0, and 0-0-5 as separate possibilities.  They are all the same.  Also, options like 4-1-0 only has one possibility because the objects are also indistinguishable so it doesn't matter which object is separate from the others.
 
Notice that I did not label the boxes, this is because they are indistinguishable.  This makes it so I do not have to list 5-0-0, 0-5-0, and 0-0-5 as separate possibilities.  They are all the same.  Also, options like 4-1-0 only has one possibility because the objects are also indistinguishable so it doesn't matter which object is separate from the others.
 +
 +
Add up these possibilities and we get 5 ways.
  
 
[[User:kduhon|kduhon]] 10:38 24, September 2008 (UTC)
 
[[User:kduhon|kduhon]] 10:38 24, September 2008 (UTC)

Revision as of 05:40, 24 September 2008

OK, so we need to put 5 indistinguishable objects into 3 indistinguishable boxes.

The easiest way to do this is to just list the different possibilities.


 5        0        0
 4        1        0
 3        2        0
 3        1        1
 2        2        1

Notice that I did not label the boxes, this is because they are indistinguishable. This makes it so I do not have to list 5-0-0, 0-5-0, and 0-0-5 as separate possibilities. They are all the same. Also, options like 4-1-0 only has one possibility because the objects are also indistinguishable so it doesn't matter which object is separate from the others.

Add up these possibilities and we get 5 ways.

kduhon 10:38 24, September 2008 (UTC)

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