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How many ways are there to put 6 balls in 3 boxes if the balls are distinguishable but the boxes are not?

 Oct 26, 2018
 #1
avatar+68 
+1

Distinguishable as in clear?

 Oct 26, 2018
 #2
avatar+183 
+1

Distinguishable as in each ball is different, instead of all of the balls having a 1 on them, they each have a different number like 1,2,3..... or they are different colors/patterns, ect.

 Oct 26, 2018
 #3
avatar+68 
0

Ok. Well, if the boxes are all the same, then, I would say, the general way to organise it would be, in number order, or, color order, or sets that coordinate the most... 

Sincerelyrose  Oct 26, 2018
 #4
avatar+98044 
+1

I think this situation  is fairly difficult to evaluate....but I believe that the answer involves something  known as "Stirling Numbers of the Second Kind"

 

The  number of ways of distributing  6  balls into 3  indistinguishable  boxes  [  assuming that one or more boxes may be empty ]   is given by this sum :

 

S2 ( 6,1)   +  S2(6,2)  + S2(6,3)  =

 

1     +           31        +    90 =

 

122  ways

 

P.S.  - If someone knows more about this....corrections are welcome  !!!!!

 

 

cool cool cool

 Oct 26, 2018
edited by CPhill  Oct 26, 2018
edited by CPhill  Oct 26, 2018
 #5
avatar+68 
+2

Lol I had the wrong idea didn't I lol

Sincerelyrose  Oct 26, 2018

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