  We discuss collision of three identical particles and derive scattering
selection rules from initial to final states of the particles. We use either
laboratory-frame, hyperspherical, or Jacobian coordinates depending on which
one is best suited to describe three different configurations of the particles:
(1) three free particles, (2) a quasi-bound trimer, or (3) a dimer and a free
particle. We summarize quantum numbers conserved during the collision as well
as quantum numbers that are appropriate for a given configuration but may
change during the scattering process. The total symmetry of the system depends
on these quantum numbers. Based on the selection rules, we construct
correlation diagrams between different configurations before and after a
collision. In particular, we describe a possible recombination of the system
into one free particle and a dimer, which can be used, for example, to identify
possible decay products of quasi-stationary three-body states
