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. Then the number of such arrangements 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

Answer 1

(c) : Out of 6 novels, 4 novels can be selected in 6C4ways.
Also out of 3 dictionaries, 1 dictionary can be selected in 3C1 ways.
Since the dictionary is fixed in the middle, we only have to arrange 4 novels which can be done in 4! ways.
Then the number of ways = 6C4 · 3C1 · 4!
= 6 ⋅ 5/2 x 3 x 24 = 1080