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EEJ MAIN Mathematics QUESTION #6934
Question 1

From a collection of 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are chosen and arranged in a row such that the dictionary always occupies the middle position. How many such arrangements exist?

  • At least 500 but less than 750
  • At least 750 but less than 1000
  • At least 1000✔️
  • Less than 500
Correct Answer Explanation

Choose 4 novels from 6: $\binom{6}{4} = 15$ ways.

Choose 1 dictionary from 3: $\binom{3}{1} = 3$ ways.

Arrange 5 books in a row with dictionary fixed in the middle: the 4 novels occupy the 4 remaining positions, giving $4! = 24$ arrangements.

Total $= 15 \times 3 \times 24 = \mathbf{1080}$

Since $1080 \geq 1000$, the answer is at least 1000.