Various criteria have been defined to evaluate the significance of sets of words, the computation of them often being difficult. We provide explicit expressions for the waiting time in such a context. In order to assess the significance of a cluster of potential binding sites, we extend them to the co-occurrence problem. We point out that these criteria values depend on a few fundamental parameters. We provide efficient algorithms to compute them, that rely on a combinatorial interpretation of the formulae. We show that our results are very tight in the so-called twilight zone and improve on previous rough approximations. One assumes that the text is generated according to a Markov stationary process. These results are developed for an extended model of consensus.