Give a combinatorial proof for $\sum_{k=1}^n k{n\choose k}=n\cdot 2^{n-1}$

Question

$$\sum_{k=1}^n k{n\choose k}=n\cdot 2^{n-1}$$

I have to prove the identity using a combinatorial proof: I think this should be my combinatorial proof.

We want to form a committee of $k$ people from a total of $n$ people.