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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 a shelf so that the dictionary is always in the middle. The number of such arrangement is:
- less than 500
- at least 500 but less than 750
- at least 750 but less than 1000
- at least 1000
Correct answer: at least 1000
Solution
To solve this, first, we choose 4 novels from 6, which can be done in 15 ways (6C4). Then, we have 1 dictionary from 3 options. The arrangement has the dictionary fixed in the middle, leaving 4 novels to arrange around it, which can be done in 4! (24 ways). Thus, the total arrangements are 15 * 3 * 24 = 1080, which is at least 1000.
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