Is there a combinatorial interpretation of the sum(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\sum_{k=0}^{n}\binom{k}{r}\binom{n-k}{m-r}[/tex] ?

If it were a sum over r instead, it would be n C m. But I don't know about this one.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Combinatorial interpretation

**Physics Forums | Science Articles, Homework Help, Discussion**