Binomial coefficient proof Prove that for any $0\lt r\lt n$ we have $$\binom nr=\binom{n-1}{r-1}+\binom{n-1}r.$$
How do prove this and what step do i take in order for it to be true? 

Ooh, one of those binomial coefficient questions that can be answered by giving a small story. I like those.
The concept to think about in this case is that of a bowl filled with $n$ balls and one of those $n$ balls is coloured pink, while the rest ($n-1$ in total) is just plain, boring white. If you take $r$ balls from this bowl, either the pink ball is one of those (in $\binom{n-1}{r-1}$ cases; can you see why?) or it isn't (in $\binom{n-1}{r}$ cases).
