  In this paper we construct a new factorized representation of the $R$-matrix
related to the affine algebra $U_{q}(\widehat{sl_{n}})$ for symmetric tensor
representations with arbitrary weights. Using the 3D approach we obtain
explicit formulas for the matrix elements of the $R$-matrix and give a simple
proof that a "twisted" $R$-matrix is stochastic. We also discuss symmetries of
the $R$-matrix, its degenerations and compare our formulas with other results
available in the literature.
