Mathematics - Permutation & Combination Question with Solution | TestHub

Given,

Mathematics paper has $20$ questions of equal marks

and have three sections $\mathrm{A}, \mathrm{B} \& \mathrm{C}$, also $\mathrm{A}$ has $8$ questions, $\mathrm{B}$ has $6$ questions and $\mathrm{C}$ 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$={}^{8}C_5·{}^{6}C_5·{}^{6}C_5+{}^{8}C_6{}^{6}C_5·{}^{6}C_4\times 2+$${}^{8}C_5·{}^{6}C_6·{}^{6}C_4\times 2+{}^{8}C_4·{}^{6}C_6·{}^{6}C_5\times 2+{}^{8}C_7·{}^{6}C_4·{}^{6}C_4$

$=56·6·6+28·6·15·2+56·15·2+70·6·2+8·15·15$

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