Q39 / 90 · JEE Main 2009 · Mathematics

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

  • A
    less than 500
  • B
    at least 500 but less than 750
  • C
    at least 750 but less than 1000
  • Correct answer
    D
    at least 1000

Solution

4 novels can be selected from 6 novels in ${ }^6 \mathrm{C}_4$ ways. 1 dictionary can be selected from 3 dictionaries in ${ }^3 \mathrm{C}_1$ ways. As the dictionary selected is fixed in the middle, the remaining 4 novels can be arranged in 4 ! ways. $\therefore$ The required number of ways of arrangement $={ }^6 \mathrm{C}_4 \times{ }^3 \mathrm{C}_1 \times 4 !=1080$

Hence, the correct answer is option: 'D'.

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