The prospects of detecting extragalactic supernovae (SNs) down to visu
al magnitudes 23-25 give us hope for observing them in the most distan
t parts of the universe. Using a Monte Carlo method of stellar populat
ion synthesis (the Scenario Machine), we compute, under standard assum
ptions of stellar evolution, the rates of SNs of various types in a mo
del galaxy and evaluate the SN rates in the universe. The expected cum
ulative distribution log N - m (number of events - stellar magnitude)
is calculated for various SN types and different star formation histor
ies in the universe. The results are also presented in terms of evolut
ion of supernova units with redshifts. Recent observational data on th
e high-redshift SN Ia rate are in good agreement with our predictions
for the relative density of baryons contained in stars at the present
time (Omega = 0.0057).