Q. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangement is
A) At least 500 but less than 750
B) At least 750 but less than 1000
C) At least 1000
D) Less than 500
Explanation
(c)
The number of ways in which 4 novels can be selected
$= \ ^{6}C_{4} = 15$
The number of ways in which 1 dictionary can be selected
$= \ ^{3}C_{1} = 3$
4 novels can be arranged in $4!$ ways
$\therefore$ The total number of ways
$= 15 \times 4! \times 3 = 15 \times 24 \times 3 = 1080$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.