JEE Main 2020 — Permutation Combination Question with Solution

$\mathrm{A}\to 5\mathrm{Q} \mathrm{B}\to 5\mathrm{Q} \mathrm{C}\to 5\mathrm{Q}$

${\mathrm{A}}_1,{\mathrm{A}}_2,{\mathrm{A}}_3,{\mathrm{A}}_4,{\mathrm{A}}_5 {\mathrm{B}}_1,{\mathrm{B}}_2,{\mathrm{B}}_3,{\mathrm{B}}_4,{\mathrm{B}}_5$
${\mathrm{C}}_1,{\mathrm{C}}_2,{\mathrm{C}}_3,{\mathrm{C}}_4,{\mathrm{C}}_5$

${\mathrm{A}}_1{\mathrm{A}}_2{\mathrm{A}}_3{\mathrm{B}}_1{\mathrm{C}}_1\Rightarrow {}^3\mathrm{C}_1\times {}^5\mathrm{C}_3\times {}^5\mathrm{C}_1\times {}^5\mathrm{C}_1=750$, where three questions are picked from any of the subject and one each from other two subjects.

${\mathrm{A}}_1{\mathrm{A}}_2{\mathrm{B}}_1{\mathrm{B}}_2{\mathrm{C}}_1\Rightarrow {}^3\mathrm{C}_2\times {}^5\mathrm{C}_2\times {}^5\mathrm{C}_2\times {}^5\mathrm{C}_1=1500$, where one question is picked from one of the subject and two each from rest of the two subjects.

$\therefore$Total number of ways$=2250$