Out of 6 distinct novels and 3 distinct dicti | vedclass

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Question

(B) The number of ways to select $4$ novels from $6$ is $\binom{6}{4} = 15$.The number of ways to select $1$ dictionary from $3$ is $\binom{3}{1} = 3$

Vedclass · Accepted Answer

At least $1000$

Vedclass · Answer

(B) The number of ways to select $4$ novels from $6$ is $\binom{6}{4} = 15$.The number of ways to select $1$ dictionary from $3$ is $\binom{3}{1} = 3$.To arrange these $5$ items ($4$ novels and $1$ dictionary) such that the dictionary is always in the middle,we fix the dictionary in the middle position in $1$ way.The remaining $4$ novels can be arranged in the remaining $4$ positions in $4!$ ways.Total arrangements $= \binom{6}{4} 	imes \binom{3}{1} 	imes 4! = 15 	imes 3 	imes 24 = 1080$.Since $1080 \geq 1000$,the correct option is $B$.

Out of $6$ distinct novels and $3$ distinct dictionaries,$4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf such that the dictionary is always in the middle. What is the number of such arrangements?

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