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 dict - Mathematics MCQ AIEEE 2009 2026 | ExamTest.live

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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:

Solution & Step-by-step Explanation

1. Selection: Choose 4 novels from 6 : (4 6) = 15 .2. Selection: Choose 1 dictionary from 3 : (1 3) = 3 .3. Arrangement: There are 5 positions. Dictionary is fixed in the middle (position 3).4. The 4 novels can be arranged in the remaining 4 positions in 4! = 24 ways.Total arrangements = 15 \times 3 \times 24 = 45 \times 24 = 1080 .This is at least 1000 .

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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:

less than 500

at least 500 but less than 750

at least 750 but less than 1000

at least 1000

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