Suppose A₁,A₂,A₃,.. , A₃₀ are thirty sets each having 5 elements and B₁,B₂ ., B_n, are n sets each with 3 elements. Let $\underset{\mathrm{i}=1}{\overset{30}{\cup }} {\mathrm{A}}_{\mathrm{i}}=\underset{\mathrm{j}=1}{\overset{\mathrm{n}}{\cup }} {\mathrm{B}}_{\mathrm{j}}=\mathrm{S}$ and each elements of S belongs to exactly 10 of the ${\mathrm{A}}_{\mathrm{i}}^{\mathrm{\prime }}\mathrm{s}$ and exactly 9 of the ${\mathrm{B}}_{\mathrm{j}}^{\mathrm{\prime }}\mathrm{s}$. Then n is equal to______