Combinatorics: n people visit k exhibitions Edit: Excuse me, the numerator of the given solution should've been a rising factorial. That said, I still don't understand where it comes from?
The question is as follows :

n friends visit k exhibitions, each person visits only 1 exhibition. Find the number of possibilities if
b) Only the number of friends who goes to each exhibition matters. Neither the order nor who goes where matters.

Now, I have the solution which would be $$\frac{[n+1]^{k-1}}{(k-1)!} $$
But I don't really understand why that is so.
If I understand that correctly, that would be a stars and bars problem, but I don't seem to grasp the concept of it.
Any help would be greatly appreciated.

Yes, it's your basic stars and bars:  You have $n$ 'stars' (the friends), and $k-1$ bars to divide the friends into $k$ groups.
So, you have $n+k-1$ objects that you line up, and there are 
$${n+k-1} \choose n$$
possible different ways to place the $n$ 'stars' in those $n+k-1$ slots.
This is not at all your formula though ...
