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:

Step-by-step solution

N 1 ,   N 2 ,   D ,   N 3 ,   N 4 N → Novels D → Dictionary D can be chosen in 3 ways N 1 → 6 N 2 → 5 N 3 → 4 N 4 → 3 Total ways = 3 × 6 × 5 × 4 × 3 = 1080