Question

From 6 different novels and 3 different dictionaries, 4 novels and a dictionary is to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then find the number of such arrangements.

Answer 1

The number of ways in which 4 novels can be selected from 6 different novels = ⁶C₄ = 15 

The number of ways in which 1 dictionary can be selected out of 3 different dictionaries = ³C₁ = 3 

Now, it is given that dictionary is always in the middle. 

Hence, the arrangement look MM D MM 

∴ Dictionary is always in the middle as the novels are different, hence they can be arranged in 4! Ways. 

Hence, total number of such arrangement = 15 × 3 × 4! 

= 15 × 3 × 4 × 3 × 2 × 1 

= 1080