Question

A candidate is required to answer $6$ questions by choosing at least one question from each section, where $1^{st}$ section consists of $4$ questions, $2^{nd}$ section consists of $3$ questions and $3^{rd}$ section consists of $2$ questions. In how many ways can he make up us choice?.

• A. $76$
• B. $80$
• C. $95$
• D. $63$

Answer 1

The correct option is A $76$

Combination of attempting the questions can be

$411,321,312,231,222,132$

where no. on the left denotes questions attempted from first section

Middle no. denotes the questions attempted from second section

The last no. of the right denotes the questions attempted from last section

So, total no. of ways of attempting question papers is

$\left({}^4{C}_4{.}^3{C}_1{.}^2{C}_1\right)+\left({}^4{C}_3{.}^3{C}_2{.}^2{C}_1\right)+\left({}^4{C}_2{.}^3{C}_3{.}^2{C}_1\right)+\left({}^4{C}_1{.}^3{C}_3{.}^2{C}_2\right)+\left({}^4{C}_2{.}^3{C}_2{.}^2{C}_2\right)+\left({}^4{C}_3{.}^3{C}_1{.}^2{C}_2\right)$

$=6+24+12+4+18+12$

$=76$