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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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What is the probability for sequence of lenght L in subset of [n]

I am trying to calculate the probability that i'll have L length sequence in a random subset of [n] when the subset size is k. for example, if n=5, k=4 and L=2 I'll have the below subsets: {2,3,4,5}, …
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