Eduprobe
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. The number of such arrangements is
At least 750 but less than 1000
At least 1000
Less than 500
At least 500 but less than 750
Solution:
Number of novels = 6
Also, the number of dictionaries = 3
Number of ways of selecting 4 novels and 1 dictionary is ⁶C₄ × ³C₁
Arrangements such that the dictionary is always in the middle is given by : NNDNN
The position of the dictionary is fixed. The novels can be arranged in 4! different ways
Total number of ways we can arrange 4 novels and 1 dictionary so that the dictionary is always in the middle = ⁶C₄ × 4! × ³C₁ = 15 × 24 × 3 = 1080
Option B is correct.