JEE Main · 2020 · 05 Sep 2020 · Shift 2 · Permutations and Combinations

Each of the three sections holds five questions, and five must be answered with at least one from every section, so the five split across the sections either as $3,1,1$ in some order or as $2,2,1$ in some order. For the $3,1,1$ pattern, choose which section supplies three ($3$ ways) and then pick the questions: $3\times \left(\genfrac{}{}{0ex}{}{5}{3}\right)\left(\genfrac{}{}{0ex}{}{5}{1}\right)\left(\genfrac{}{}{0ex}{}{5}{1}\right)=3\times 10\times 5\times 5=750$. For the $2,2,1$ pattern, choose which section supplies one ($3$ ways): $3\times \left(\genfrac{}{}{0ex}{}{5}{2}\right)\left(\genfrac{}{}{0ex}{}{5}{2}\right)\left(\genfrac{}{}{0ex}{}{5}{1}\right)=3\times 10\times 10\times 5=1500$. Altogether $750+1500=2250$ ways.