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

ANotSmartPerson Oct 26, 2018

#2**+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.

ANotSmartPerson Oct 26, 2018

#3**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**+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 !!!!!

CPhill Oct 26, 2018