# Full of $$\binom{\text{summations}}{\text{combinations}}$$

Discrete Mathematics Level 4

The sum $\binom{2014}{1565}+\sum_{k=1}^{333} \binom{k+2013}{k+1565}+\sum_{k=1}^{48} \binom{k+2346}{1897}$can be expressed in the form $$\binom{x}{y}$$, where $$x$$ and $$y$$ are four-digit integers. Find the value of $$x-y.$$

×