In an examination of Mathematics paper, there are 20 questions of...

Given,

Mathematics paper has $20$ questions of equal marks

and have three sections $A, B \text{ and } C$, also $A$ has $8$ questions, $B$ has $6$ questions and $C$ has $6$ questions,

Now, if $4$ questions from each section are selected,

then remaining $3$ questions can be selected either in $( 1, 1, 1 )$ or $( 3, 0, 0 )$ or $( 2, 1, 0 )$ {as we have already selected $4 \times 3 = 12$ questions}

So, the total ways will be$= C5 8 \cdot C5 6 \cdot C5 6 + C6 8 C5 6 \cdot C4 6 \times 2 +$$C5 8 \cdot C6 6 \cdot C4 6 \times 2 + C4 8 \cdot C6 6 \cdot C5 6 \times 2 + C7 8 \cdot C4 6 \cdot C4 6$

$= 56 \cdot 6 \cdot 6 + 28 \cdot 6 \cdot 15 \cdot 2 + 56 \cdot 15 \cdot 2 + 70 \cdot 6 \cdot 2 + 8 \cdot 15 \cdot 15$

$= 2016 + 5040 + 1680 + 840 + 1800 = 11376$