Proof binomial coefficient by induction i have to show that 
$\sum_{j=0}^n 
\binom{n}{j} * 
\binom{m}{k-j} = 
\binom{n+m}{k}$
is valid.
I tried to do it by induction, the induction beginning fits, but unfortunately, I don't know how to the induction step. I have been failing now for hours, is there someone who can help me, please?

It's coefficient of $x^k$ in $(1+x)^{m+n}$ or see Vandermondes identity as I see you don't need binomial proof .
