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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. Then the number of such arrangement is:
- at least 500 but less than 750
- at least 750 but less than 1000
- at least 1000
- less than 500
Correct answer: at least 1000
Solution
The arrangement requires selecting 4 novels from 6 and 1 dictionary from 3, with the dictionary fixed in the middle position. The number of ways to choose the novels is given by combinations, and the total arrangements of the novels around the dictionary lead to a calculation that exceeds 1000, confirming option C is correct.
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