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# Probability Question

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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
+75
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Distinguishable as in clear?

Oct 26, 2018
#2
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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
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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
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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

Oct 26, 2018
edited by CPhill  Oct 26, 2018
edited by CPhill  Oct 26, 2018
#5
+75
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Lol I had the wrong idea didn't I lol

Sincerelyrose  Oct 26, 2018