Mathematics - Functions Question with Solution | TestHub

Let ${\mathrm{A}}_1,{\mathrm{A}}_2,{\mathrm{A}}_3,\dots ,{\mathrm{A}}_{40}$ are 40 sets each with 7 elements and ${\mathrm{B}}_1,{\mathrm{B}}_2,\dots ,{\mathrm{B}}_{\mathrm{n}}$ are n sets each with 7 elements. If ${\bigcup }_{\mathrm{i}=1}^{40}{\mathrm{A}}_{\mathrm{i}}={\bigcup }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{B}}_{\mathrm{j}}=\mathrm{S}$ and each element of S belongs to exactly ten of ${\mathrm{A}}_{\mathrm{i}}$ 's and exactly 9 of ${\mathrm{B}}_{\mathrm{j}}$ 's, then n equals