english is not my first language, so sorry for any typos. I'm a first year math student, and I'm having problems understanding the meaning of this identity
$\binom{p+r+1}{q} = \sum_{i=0}^q (\binom{p-i}{q-i}\binom{r+i}{i})$
I tried to formulate a problem using subsets, but i can't visualize the how choosing q objects from p+r+1 would be the same as to what's on the right side. I also tried to formulate one using a grid, but the draw got confusing really fast. If someone has a combinatorial argument to explain or at least help me understand the meaning of this I would be very thankful.