# What's the interpretation of $\sum_{i,j} i \cdot j \cdot \binom{2n}{i}\cdot \binom{2n}{j} \cdot \binom{2n}{3n-i-j}$?

I'm having problems with finding the combinatorial interpretation of this sum: $$\sum_{i,j} i \cdot j \cdot \binom{2n}{i}\cdot \binom{2n}{j} \cdot \binom{2n}{3n-i-j}$$

• maybe the Sigma sign is the problem? it's $\sum_{i=0}^{n} \sum_{j=0}^{n}$. – Alex Jun 13 '14 at 15:00
• Are you sure that the last binomial term has $3n-i-j$ and not $2n-i-j$? – Anurag A Jun 13 '14 at 15:46