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.

  • $\begingroup$ Google the hockey stick identity. $\endgroup$ – Don Thousand Oct 9 '18 at 22:53
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    $\begingroup$ An algebraic proof is quite easy, but you want a combinatorial argument. Right ? $\endgroup$ – Donald Splutterwit Oct 9 '18 at 23:09
  • $\begingroup$ @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. $\endgroup$ – Axl_128 Oct 9 '18 at 23:39

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