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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. Then the number of such arrangements is

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

## The correct option is B at least 1000Let N1N2N3…N6 be novels and D1D2D3 be dictionariesThe number of ways =6C4×3C1×(4!)N N D N NHere, 6C4 denotes the selection of 4 novels out of 6,3C1 denotes the selection of 1 dictionary out of 3 and (4!) denotes the rearrangement of 4 novels as dictionary will always be in the middle.=15×3×24=1080 Hence, option 'D' is correct.

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