combinatorics - Fermat's Combinatorial Identity: How to prove combinatorially?

$$\binom{r}{r} + \binom{r+1}{r} + \binom{r+2}{r} + \dotsb + \binom{n}{r} = \binom{n+1}{r+1}$$

I don't have much experience with combinatorial proofs, so I'm grateful for all the hints.

(Presumptive) Source: Theoretical Exercise 1.11, P18, A First Course in Pr, 8th Ed, by S Ross