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  6C4 ways. One dictionary can be selected from 3 dictionaries in  3C1 ways.

    As the dictionary selected is fixed in the middle, the remaining 4 novels can be arranged in 4! ways.

     The required number of ways of arrangement =6C4×3C1×4!=1080

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