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**How many ways can you place 10 identical balls into 3 identical boxes? Note: Up to two boxes may be empty.**

I approached this problem as:

Let B represent ball

Let 0 represent nothing (empty)

|box wall| 0 0 B B B B B B B B B B |box wall|

So, there must be two other box walls that must be inserted, and they can be inserted in these places:

|box wall| 0 0 B B B B B B B B B B |box wall|

^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

So, that would make [tex]_{11}C _{2}=55[/tex]. However, my teacher says it's supposed to be 66. Could someone please explain why? Thanks.