So my Prof give me this Statement to proof and i have no idea how i could solve it tho.
$$S(k,n)=S(k−1,n−1) + n \cdot S(k−1,n)$$
My task is to prove it and as hint he said: Use The binomial coefficients.
I have tried to solve it with induction, but it does not work though.
Anyone have an idea how to do it? or like a website where I could look up?
It looks like $S(k, n)$ is supposed to represent the number of ways of placing $k$ distinct objects in $n$ nonempty subsets.
Hint: For the recurrence, the $k$th object can either be placed in a separate subset from the $n - 1$ nonempty subsets into which the other $k - 1$ objects have been placed or it can be placed in one of the $n$ nonempty subsets into which the other $k - 1$ objects have been placed.