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
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a
less than 500
b
at least 500 but less than 750
c
at least 750 but less than 1000
d
at least 1000
answer is D.
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Detailed 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