Geodesic
On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a~random sequence
Diskretnaya Matematika, Tome 20 (2008) no. 4, pp. 113-119.

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In a long enough sequence of discrete random variables, as a rule, an $s$-tuple exists of nontrivial structure, that is, a tuple with at least one repeated symbol. We consider the case where the sequence consists of $n+s-1$ independent random variables taking the values $1,\dots,N$ with equal probabilities. It is shown that as $n\to\infty$, $ns^3N^{-2}\to0$ the probability of that in the sequence $s$-tuples exist with the same nontrivial structure is equal to $1-(1+n/N)^se^{-sn/N}(1+o(1))$. 
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V. G. Mikhailov. On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a~random sequence. Diskretnaya Matematika, Tome 20 (2008) no. 4, pp. 113-119. http://geodesic.mathdoc.fr/item/DM_2008_20_4_a9/

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[2] Barbour A. D., Holst L., Janson S., Poisson approximation, Oxford Univ. Press, Oxford, 1992 | MR | Zbl