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. Then the number of such arrangements is
at least 500 but less than 750
at least 1000
at least 750 but less than 1000
less than 500
Solution:
Let N1, N2, N3…N6 be novels and D1, D2, D3 be dictionaries
The number of ways = ⁶C₄ × ³C₁ × (4!)
N N D N N
Here, ⁶C₄ denotes the selection of 4 novels out of 6, ³C₁ denotes the selection of 1 dictionary out of 3 and (4!) denotes the rearrangement of 4 novels as the dictionary will always be in the middle.
= 15 × 3 × 24 = 1080
Hence, option 'B' is correct.