Number of ways to arrange $3$ rocks in $6$ boxes 
Possible Duplicate:
Unique ways to keep N balls into K Boxes? 

This question may be sound stupid, but we really cant figure it out. We have 3 rocks and 6 boxes. All the rocks have to be in the boxes. The rocks can be all in one box or spread out. 
How many unique combinations can we possible have?
I made a spreadsheet of this 
https://docs.google.com/spreadsheet/ccc?key=0AjBAKweB5syRdDFVeE5qNVJqT3F5RE9heERvYVBWdnc&hl=en_US
i came up with 53. I am missing some? please let me know.
The question to this problem is whats the equation. How do we come up with this number without the spreadsheet so i can apply it to a another set of questions.

It all depends on what you count as a different pattern.
If each rock and each box count as different you can put each rock in one of six boxes so you get $6^3$.  The number of ways of having each rock in a different box is $6\times 5 \times 4$, so the probability is $\frac{5}{9}$.
If the rocks all look the same and the boxes look the same there are $3$ ways: three boxes with one rock each and three empty; a box with two, a box with one and four with none; or a box with three and five with none. The probability of having each rock in a different box becomes $\frac{1}{3}$ if each pattern is equally likely.
Or perhaps the boxes look the same and the rocks different, or the boxes are different but the rocks look the same, and you have two more possible answers.   You seem to want the last of these, and it is not difficult, so why not show us what you think the answer might be.
