From 6 different novels and 3 different dicti | vedclass

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

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atleast $1000$

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(C) Step $1$: Select $4$ novels from $6$ different novels. This can be done in $^6C_4$ ways.$^6C_4 = \frac{6 	imes 5}{2 	imes 1} = 15$ ways.Step $2$: Select $1$ dictionary from $3$ different dictionaries. This can be done 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.Number of ways to arrange $4$ novels = $4! = 4 	imes 3 	imes 2 	imes 1 = 24$.Step $4$: Total number of arrangements = (Ways to select novels) $	imes$ (Ways to select dictionary) $	imes$ (Ways to arrange novels) = $15 	imes 3 	imes 24 = 1080$.

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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