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(A) We have $5$ Mathematics,$4$ Physics,and $2$ Chemistry books. Since books of the same subject must be kept together,we treat each subject group as

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$3! 	imes 5! 	imes 4! 	imes 2!$

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(A) We have $5$ Mathematics,$4$ Physics,and $2$ Chemistry books. Since books of the same subject must be kept together,we treat each subject group as a single unit. There are $3$ such units (Mathematics group,Physics group,and Chemistry group),which can be arranged among themselves in $3!$ ways. Within their respective groups,the $5$ Mathematics books can be arranged in $5!$ ways,the $4$ Physics books in $4!$ ways,and the $2$ Chemistry books in $2!$ ways. Therefore,the total number of arrangements is $3! 	imes 5! 	imes 4! 	imes 2!$.

There are $11$ distinct books on a shelf,consisting of $5$ Mathematics,$4$ Physics,and $2$ Chemistry books. In how many ways can they be arranged such that books of the same subject are always kept together?

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