How many ways are there to put 6 balls in 3 boxes if the balls are distinguishable but the boxes are not?
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.
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 =
P.S. - If someone knows more about this....corrections are welcome !!!!!