+0  
 
+1
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avatar+426 

How many ways are there to put 4 balls in 3 boxes if the balls are distinguishable but the boxes are not?

 Oct 2, 2020
 #1
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With no restrictions and empty boxes are allowed, you have:

 

[4 + 3 - 1 ] nCr [3 - 1] = 6 C 2 = 15 ways.

 Oct 2, 2020
 #2
avatar+426 
+1

That is incorrect sorry

 Oct 2, 2020
 #3
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This is a case of of 4 distinct balls into 3 identical boxes: Case 1 uses “Stirling Numbers of the 2nd kind”. Case 2 uses “Bell numbers”

Case 1:
If we consider that ALL the Boxes Should have Balls, the Solution is:  = 6 ways

Case 2:
If we consider that Boxes Can be left Empty, then the Solution is: 

=0 + 1 + 7 + 6 = 14 ways

 Oct 2, 2020

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