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We consider three combinatorial problems covered by generalised allocation scheme: sampling of balls from an urn that contains balls of various colours; random forests; and random permutations with given number of cycles. For these problems, we present limit distributions of the number of pairs of balls of the same colour; of the number of paths in a forest; and of the number of simple (non-closed) paths in the permutation graph respectively.

Limit distribution of the number of pairs in generalised allocation scheme