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Question

# 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 arrangements is

A
At least 500 but less than 750
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B
At least 750 but less than 1000
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C
At least 1000
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D
Less than 500
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Solution

## The correct option is C At least 1000Number of novels =6Also, the number of dictionaries =3Number of ways of selecting 4 novels and 1 dictionary is 6C4×3C1Arrangements such that the dictionary is always in the middle is given by :NNDNNThe position of the dictionary is fixed. The novel can be arranged in 4! different waysTotal number of ways we can arrange 4 novels and 1 dictionary so that dictionary always in the middle =6C4×4!×3C1=15×24×3=1080Option C is correct.

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