How do I calculate the number of options for $k$ different balls in $n$ cells, with at least $1$ ball in each cell? 

Lets say $6$ different balls in $3$ different cells, with at least $1$ ball in each cell. 

like this: 
$$x\_1+x\_2+x\_3 = 6$$

I would like to see an explanation please and not just the answer.

Thanks!