Limit distributions of the number of not appeared $s$-tuples in a multinomial scheme

Let $\mu_0(s,n,p_1\dots,p_N)$ be the number of not appeared $s$-tuples in a sequence of $n+s-1$ independent trials, at each trial the probability of event $i$ being $p_i$, $i=1,\dots,N$.
We consider asymptotic behaviour of $\mu_0(s,n,p_1\dots,p_N)$ as $n,N$ and $n/N\to\infty$.
In particular, we obtain conditions under which the distributions of $\mu_0(s,n,p_1\dots,p_N)$ converge to a Poisson distribution without assuming $p_1\dots,p_N$ to be close to $1/N$.