Let (I_1, I_2,..., I_k) be a random k-tuple of subintervals of the discrete interval [1, n], and L_n the random variable that measures the size of their insersection. We derive the exact and asymptotic distribution of L_n under the assumption of equally likely drawn k-tuples. The enumeration of such k-tuples and refinements of the given statistic lead to interesting relations to other topics, like octahedral numbers and bipartite graphs.
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