Help with a combinatorial identity

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.

• Google the hockey stick identity. – Don Thousand Oct 9 '18 at 22:53
• An algebraic proof is quite easy, but you want a combinatorial argument. Right ? – Donald Splutterwit Oct 9 '18 at 23:09
• @RushabhMehta, I did, but if I should use it to prove it (or if they are the same but written differently) I can't see how, DonaldSplutterwit yes, I need it using arguments. – Axl_128 Oct 9 '18 at 23:39