In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : A,B and C. A…

Given,

Mathematics paper has $20$20 questions of equal marks

and have three sections A,B&C, also $A$A has $8$8 questions, $B$B has $6$6 questions and $C$C has $6$6 questions,

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

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

So, the total ways will be$=C58\cdot C56\cdot C56+C68C56\cdot C46\times 2+$=C58⋅C56⋅C56+C68C56⋅C46×2+$C58\cdot C66\cdot C46\times 2+C48\cdot C66\cdot C56\times 2+C78\cdot C46\cdot C46$C58⋅C66⋅C46×2+C48⋅C66⋅C56×2+C78⋅C46⋅C46

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

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