Question

From $6$ different novels and $3$ different dictonaries, $4$ 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. at least $750$ but less than $1000$
• B. at least $500$ but less than $750$
• C. less than $500$
• D. at least $1000$

Answer 1

The correct option is D at least $1000$

Dictionary can be chosen in ${}^3{C}_1=3$ ways
Novels can be arranged in ${}^6{C}_{4}4!=360$ ways
$N=3\times 360=1080$