  The Multi-particle technique has been used to unravel the nature of the
long-range collectivity in small collision systems. A large three-particle
mixed-harmonic correlation signal was recently observed by the ATLAS
Collaboration, but the role of non-flow correlations is not yet studied. We
estimate the influence of non-flow correlations to the three-particle
correlators in $pp$ and $p$+Pb collisions using PYTHIA and HIJING models, and
compare with the ATLAS results. The large non-flow effects from the jet and
dijet production is found to be largely suppressed in $p$+Pb collisions using
the subevent cumulant method by calculating the azimuthal correlation between
two or more longitudinal pseudorapidity ranges. Depending on the experimental
subevent method, however, the non-flow effects may still be significant in $pp$
collisions.
