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 :
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 :
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Choose the books, then arrange the four novels in the four non-middle positions.
Updated On: Nov 11, 2026
- at least 750 but less than 1000
- at least 1000
- less than 500
- at least 500 but less than 750
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The Correct Option is B
Solution and Explanation
Select 4 novels from 6: \(\binom64=15\) ways. Select 1 dictionary from 3: \(3\) ways.
The dictionary must occupy the middle (3rd) position of the 5 places; the 4 novels can be arranged in the remaining 4 places in \(4!=24\) ways.
Total \(=15\times3\times24=1080\), which is at least 1000.
Answer: (2) at least 1000
The dictionary must occupy the middle (3rd) position of the 5 places; the 4 novels can be arranged in the remaining 4 places in \(4!=24\) ways.
Total \(=15\times3\times24=1080\), which is at least 1000.
Answer: (2) at least 1000
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