Question

A question paper is divided into two parts $A$ and $B$ and each part contains $5$ questions. The number of ways in which a candidate can answer $6$ questions selecting at least two questions from each part is:

• A. $80$
• B. $100$
• C. $200$
• D. None of these

Answer 1

The correct option is C $200$

	$\left(A\right)$	$\left(B\right)$
	$\left(5question\right)$	$\left(5question\right)$
$\left(i\right)$	$2$	$4$	$=6$
$\left(ii\right)$	$3$	$3$	$=6$
$\left(iii\right)$	$4$	$2$	$=6$

There are two section and the candidates has to answer at least $2$ question from each section with total of $6$ questions.

So, there are three followign ways.

$\left(i\right)$ no of ways $\Rightarrow$ selecting $2$ questions from section $A$ and $4$ questions from sections $B$

${\Rightarrow }^5{C}_2{\times }^5{C}_4\Rightarrow 10\times 5\Rightarrow 50$

$\left(ii\right)$ no. of ways $\Rightarrow$ selecting $3$ questions from each section.

${\Rightarrow }^5{C}_3{\times }^5{C}_3\Rightarrow 10\times 19=100$

$\left(iii\right)$ no. of ways $\Rightarrow$ selecting $4$ from section $A$ and $2$ from section $B$

${\Rightarrow }^5{C}_4{\times }^5{C}_2\Rightarrow 5\times 10\Rightarrow 50$

$\therefore$ Total no. of ways $=50+100+50=200$.