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 arrangements is

Step-by-step solution

4 novels can be selected from 6 novels in ^6 C ₄ ways. 1 dictionary can be selected from 3 dictionaries in ^3 C ₁ ways. As the dictionary selected is fixed in the middle, the remaining 4 novels can be arranged in 4 ! ways. The required number of ways of arrangement = ^6 C ₄ ^3 C ₁ 4 !=1080