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 arrangements is

• A. less than $500$
• B. atleast $500$ but less than $750$
• C. atlease $750$ but less than $1000$
• D. at least $1000$

Answer 1

The correct option is D at least $1000$

$6$ Novels $+3$ dictioneries

$N_1$ $N_2$ $D_1$ $N_3$ $N_4$

No of possible arrangements $\Rightarrow$

$\left({}^6{C}_4\right)\left({}^3{C}_1\right)\left(\angle 4\right)\to$ Arrangement Selection of

Novels Selection of Dictionary of Novels

$=1080$

$\therefore$ At least $1000$