  We define finite multiple zeta values (FMZVs) associated with some
combinatorial objects, which we call 2-colored rooted trees, and prove that
FMZVs associated with 2-colored rooted trees satisfying certain mild
assumptions can be written explicitly as $\mathbb{Z}$-linear combinations of
the usual FMZVs. Our result can be regarded as a generalization of Kamano's
recent work on finite Mordell-Tornheim multiple zeta values. As an application,
we will give a new proof of the shuffle relation of FMZVs, which was first
proved by Kaneko and Zagier.
