  We study the explicit relation between violation of Bell inequalities and
bipartite distillability of multi-qubit states. It has been shown that even
though for $N\ge 8$ there exist $N$-qubit bound entangled states which violates
a Bell inequality [Phys. Rev. Lett. {\bf 87}, 230402 (2001)], for all the
states violating the inequality there exists at least one splitting of the
parties into two groups such that pure-state entanglement can be distilled
[Phys. Rev. Lett. {\bf 88}, 027901 (2002)]. We here prove that for all
$N$-qubit states violating the inequality the number of distillable bipartite
splits increases exponentially with $N$, and hence the probability that a
randomly chosen bipartite split is distillable approaches one exponentially
with $N$, as $N$ tends to infinity. We also show that there exists at least one
$N$-qubit bound entangled state violating the inequality if and only if $N\ge
6$.
