Higher order animals show the remarkable ability to flexibly adapt their behavior according to the context. The execution of complex cognitive tasks can be modeled as a series of event driven transitions between mental states, each encoding a certain disposition to behavior or a specific sensori-motor decision. In this work, we hypothesize that these mental states are instantiated neuronally by recurrent circuit dynamics, in the form of stable attractors of the neural activity. We show that the mathematical conditions for the attractors and the event driven transitions can be satisfied only if neurons are selective to combinations of internal mental states and sensory stimuli. One possible way to generate such mixed selectivity is to introduce neurons whose afferent connections have random synaptic strengths. This approach has at least three highly desirable features. First, in spite of the combinatorial explosion of possible neurons with mixed selectivity, the number of needed randomly connected neurons grows only linearly with the number of relevant task events and contexts, which makes a reasonably sized network able to execute extremely complex cognitive tasks. Second, the firing patterns of neurons of the simulated proposed network, capture several aspects of the activity recorded in prefrontal cortex and other brain areas involved in a complex cognitive processes. The activity is self-sustaining in the absence of events, rule selective, and highly heterogeneous. Third, the introduction of randomly connected neurons accelerates the convergence of learning algorithms and it can be exploited to rapidly learn complex behavioral tasks. In conclusion we think that mixed selectivity, so widely observed in the living brain, can be an important and general functional principle for executing complex cognitive tasks.