I perform a statistical study of the rate at which close binaries consisting of a white dwarf and a main-sequence companion are formed by common envelope evolution. Using a Monte Carlo technique, a population of zero-age binaries is constructed, with likely distributions over primary mass, separation, and mass ratio. The evolution of these systems is followed using simple analytic fits to more detailed evolutionary calculations. If a binary undergoes a common envelope phase during its evolution, the outcome is predicted with the help of the standard assumption that a fraction α of the gravitational binding energy between the secondary and the giant core is available to eject the envelope. If it is assumed that the common envelope phase is accompanied by the formation of a planetary nebula, we find that for values of α close to 1 the observed number of planetary nebulae containing a double core with an orbital period shorter than 1 day is in reasonable agreement with our predictions. The distribution of primary masses in these double cores yields an estimate of α since the maximum in this distribution is shown to be well correlated with α, but uncertain observational selection effects make this test difficult to use in practice. The distribution of orbital periods contains information on a, but a larger number of observed periods is needed to be able to derive significant constraints. The lower mass limit on the primary mass in cataclysmic variables is consistent with a value of α larger than 0.1. A distribution over initial mass ratio in wide, low-mass pre-common envelope binaries that is strongly biased toward equal masses is less compatible with the observed secondary masses of the binary cores of planetary nebulae than an initial mass ratio distribution that results from picking both stars individually from the same initial mass function.
