It is commonly believed that information processing in cortical networks involves the collective spiking activity of neuronal assemblies. Nevertheless, due to current technical limitations in multielectrodes recording methods, it is not possible to tackle this issue with direct experimental measurements. In this study we simulate spiking activity of large ensembles of cells focusing on the temporal correlation properties of the neuronal dynamics, and demonstrate that transient, fast synchronization of large groups of cells is a natural phenomenon of the cortical activity. To prove this result we use a statistical approach (based on combinatorics), and knowledge derived from a previous research work [A. Benucci et al., Phys. Rev. E 68, 041905 (2003)]. We quantify the degree of synchronous activity by computing a lower bound for the fraction of cells participating in fast (few milliseconds) synchronous events. Finally we discuss the implications of the results found in terms of cortical coding mechanisms.