The number of ways in which $n$ different things can be distributed into $r$ different groups is coefficient of $x^n$ in $n!(e^x-1)^r$?

Question

This is the question of combination.

I have tried this but how can the binomial expansion can result our need? How we can proof the formula:

The number of ways in which n different things can be distributed into $r$ different groups is coefficient of $x^n$ in $n!(e^x-1)^r$?