We first study holomorphic isometries from the Poincaré disk into the product of the unit disk and the complex unit n -ball for n ≥ 2 . On the other hand, we observe that there exists a holomorphic isometry from the product of the unit disk and the complex unit n -ball into any irreducible bounded symmetric domain of rank ≥ 2 which is not biholomorphic to any type- IV domain. In particular, our study provides many new examples of holomorphic isometries from the Poincaré disk into irreducible bounded symmetric domains of rank at least 2 except for type- IV domains.