  In this paper we study the non-local properties of permutation symmetric
states of n-qubits. We extend the bipartite Hardy paradox and the associated
CH-inequality to n-party permutation symmetric states to show that all
symmetric states exhibit non-locality. Natural extensions of both the paradoxes
and the inequalities are developed which relate different entanglement classes
to different non-local features. We define inequalities which are violated by
all states of one entanglement class, whereas there are states outside that
class which do not violate.
