  Here we report on a study aimed to explore the dependence of the genuine
multiparticle correlations on the number of sources while the influence of
other possible factors affecting the multihadron production is avoided. The
analysis utilised the normalised cumulants, calculated in three-dimensional
phase space, of the reaction e+e- -> Z -> hadrons using a large Monte Carlo
event sample. The multi-sources reactions were simulated by overlaying a few
independent single e+e- annihilation events. It was found that as the number of
sources S increases, the cumulants do not change significantly their structure,
but those of an order q>2 (i.e. more than 2 pions) decrease fast in their
magnitude. This reduction can be understood in termsof combinatorial
considerations of source mixing which dilutes the correlations by a factor of
about 1/S^{q-1} which can also serve as a method to estimated the number of
sources. This expected suppression is well reproduced by recent cumulant
measurements in hadron and nucleus induced reactions both in one (rapidity) and
two (rapidity vs. azimuthal angle) dimensions. The diminishing genuine
correlations effect should also appear in other dynamical correlations like the
Bose-Einstein in e+e- -> W+W- -> hadrons and in nucleus-nucleus reactions.
