Question

From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangement is

• A. At least $750$ but less than $1000$
• B. At least $1000$
• C. Less than $500$
• D. At least $500$ but less than $750$

Answer 1

The correct option is B At least $1000$

Select 4 novels from 6 novels ${=}^6{C}_4$

Select 1 dictionary from 3 dictionaries= $={}^3{C}_1$

So, arrangement

$\begin{array}{c}={}^6{C}_4{\times }^3{C}_1\times 4!\times 1!\\ =1080\end{array}$