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

We have to form a row of exactly five books that looks like
  novel - novel - dictionary - novel - novel,

because the dictionary is required to occupy the middle (third) position.

Step 1 - Choose the books
• Select 4 novels out of the 6 available: $$\binom{6}{4}=15$$ choices.
• Select 1 dictionary out of the 3 available: $$\binom{3}{1}=3$$ choices.

Step 2 - Arrange the chosen books
• The single chosen dictionary is fixed in the middle and therefore has only 1 possible place.
• The 4 chosen novels must fill the remaining four positions, which can be done in $$4! = 24$$ different ways.

Step 3 - Total number of arrangements
Multiply the numbers from Steps 1 and 2:
Total arrangements $$= 15 \times 3 \times 24 = 1080.$$

Since $$1080 \ge 1000,$$ the correct range is “at least 1000.”

Option D which is: at least $$1000$$