We have measured the photon statistics of random lasers with resonant feedback. With an increase of the pump intensity, the photon number distribution in a single mode changes continuously from Bose-Einstein distribution at the threshold to Poisson distribution well above the threshold. The second-order correlation coefficient drops gradually from 2 to 1. By comparing the photon statistics of a random laser with resonant feedback and that of a random laser with nonresonant feedback, we illustrate very different lasing mechanisms for the two types of random lasers.