  We study scalar products of Bethe vectors in integrable models solvable by
nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(2|1)$ symmetry.
Using explicit formulas of the monodromy matrix entries multiple actions onto
Bethe vectors we obtain a representation for the scalar product in the most
general case. This explicit representation appears to be a sum over partitions
of the Bethe parameters. It can be used for the analysis of scalar products
involving on-shell Bethe vectors.
  As a by-product, we obtain a determinant representation for the scalar
products of generic Bethe vectors in integrable models with
$\mathfrak{gl}(1|1)$ symmetry.
