  Let $C_n$ be a cyclic group of order $n$. A sequence $S$ of length $\ell$
over $C_n$ is a sequence $S = a_1\boldsymbol\cdot a_2\boldsymbol\cdot
\ldots\boldsymbol\cdot a_{\ell}$ of $\ell$ elements in $C_n$, where a
repetition of elements is allowed and their order is disregarded. We say that
$S$ is a zero-sum sequence if $\Sigma_{i=1}^{\ell} a_i = 0$ and that $S$ is a
zero-sum free sequence if $S$ contains no zero-sum subsequence.
  Let $R$ be a random subset of $C_n$ obtained by choosing each element in
$C_n$ independently with probability $p$. Let $N^R_{n-1-k}$ be the number of
zero-sum free sequences of length $n-1-k$ in $R$. Also, let $N^R_{n-1-k,d}$ be
the number of zero-sum free sequences of length $n-1-k$ having $d$ distinct
elements in $R$. We obtain the expectation of $N^R_{n-1-k}$ and $N^R_{n-1-k,d}$
for $0\leq k\leq \big\lfloor \frac{n}{3} \big\rfloor$. We also show a
concentration result on $N^R_{n-1-k}$ and $N^R_{n-1-k,d}$ when $k$ is fixed.
