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(C) Step $1$: Select $4$ novels from $6$ different novels in $^6C_4$ ways.$^6C_4 = \frac{6 	imes 5}{2 	imes 1} = 15$ ways.Step $2$: Select $1$ dicti

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at least $1000$

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(C) Step $1$: Select $4$ novels from $6$ different novels in $^6C_4$ ways.$^6C_4 = \frac{6 	imes 5}{2 	imes 1} = 15$ ways.Step $2$: Select $1$ dictionary from $3$ different dictionaries in $^3C_1$ ways.$^3C_1 = 3$ ways.Step $3$: Arrange the $4$ selected novels and $1$ dictionary in a row such that the dictionary is always in the middle.Since the dictionary is fixed in the middle,we only need to arrange the $4$ novels in the remaining $4$ positions.The number of ways to arrange $4$ novels is $4! = 24$.Step $4$: Total number of arrangements = $^6C_4 	imes ^3C_1 	imes 4! = 15 	imes 3 	imes 24 = 1080$.

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 :

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