If $4$ questions from each section are selected

Remaining $3$ questions can be selected either in $(1,1,1)$ or $(3,0,0)$ or $(2,1,0)$

$\therefore$ Total ways $={ }^8 \mathrm{c}_5 \cdot{ }^6 \mathrm{c}_5 \cdot{ }^6 \mathrm{c}_5+{ }^8 \mathrm{c}_6{ }^6 \mathrm{c}_5 \cdot{ }^6 \mathrm{c}_4 \times 2+$

${ }^8 \mathrm{c}_5 \cdot{ }^6 \mathrm{c}_6 \cdot{ }^6 \mathrm{c}_4 \times 2+{ }^8 \mathrm{c}_4 \cdot{ }^6 \mathrm{c}_6 \cdot{ }^6 \mathrm{c}_5 \times 2+{ }^8 \mathrm{c}_7 \cdot{ }^6 \mathrm{c}_4 \cdot{ }^6 \mathrm{c}_4 $

$ =56 \cdot 6 \cdot 6+28 \cdot 6 \cdot 15 \cdot 2+56 \cdot 15 \cdot 2+70 \cdot 6 \cdot 2 $

$ +8 \cdot 15 \cdot 15 $

$ =2016+5040+1680+840+1800=11376$