For a finite abelian group $G$ with $|G| = n$, the Davenport Constant $DA(G)$ is defined to be the least integer $k$ such that any sequence $S$ with length $k$ of elements in $G$ has a non-empty $A$ weighted zero-sum subsequence. For certain sets $A$, we already know the precise value of constant corresponding to the cyclic group $\mathbb{Z} / n \mathbb{Z}$. But for different group $G$ and $A$, the precise value of it is still an open question. We try to find out bounds for these combinatorial invariant for random set $A$. We got few results in this connection. In this talk I would like to present those results and discuss about an extremal problem related to this combinatorial invariant.

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