+118609 I have got an old one of Mellie's question
I think Alan may have answered it with sigma notation. Thanks Alan 
And I know Nauseated answered it but he never explained his answer!
Thanks Nauseated but an answer without an explanation is of little value.
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It was
How many ways can you distribute 12 unlabelled b***s into 9 labelled boxes in such a way as each box receives at least one ball.
Well the question can be simplified a little because since every box must have at least on ball it is only the remaining 3 b***s that must be placed into a box or boxes.
Here are the 9 boxes they are different from one another but the order makes no difference
| | | | | | | | |
and here are the 3 b***s * * *
I shall put them together
***|||||||||
The b***s will go into the container on the right.
So we need to know how many postions the b***s (*s) can go in in relation to the boxes ( | )and each other.
So there are 3+9-1 =11 objects
The last bar doesn't count because it is set - it has to come last !
We need to know how many ways we can choose 3 of them because those 3 will be the b***s.
that is 11C3 = 165 way
OR similarly we could say that we have 11 positions and we want to chose 8 of those positions to be the boxes. This would be 11C8 = 165 ways.
This kind of problem is called a stars and bars problem. You can see why
