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

# 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

1. A

less than 500

2. B

at least 500 but less than 750

3. C

at least 750 but less than 1000

4. D

at least 1000

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### Solution:

Four novels can be selected from 6 novels in  ways. One dictionary can be selected from 3 dictionaries in  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 ${=}^{6}{\mathrm{C}}_{4}{×}^{3}{\mathrm{C}}_{1}×4!=1080$

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