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Let $L_f$ be a link of an isolated hypersurface singularity defined by aweighted homogenous polynomial $f.$ In this article, we give ten examples of$2$-connected seven dimensional Sasaki-Einstein manifolds $L_f$ for which$H_{3}(L_f, \mathbb{Z})$ is completely determined. Using the Boyer-Galickiconstruction of links $L_f$ over particular K\"ahler-Einstein orbifolds, weapply a valid case of Orlik's conjecture to the links $L_f $ so that one isable to explicitly determine $H_{3}(L_f,\mathbb{Z}).$ We give ten such newexamples, all of which have the third Betti number satisfy $10\leqb_{3}(L_{f})\leq 20$.

Sasaki-Einstein 7-Manifolds, Orlik Polynomials and Homology