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Question Number 180027 by mr W last updated on 06/Nov/22

$$\mathrm{There}\mathrm{are}4\mathrm{identical}\mathrm{mathematics}$$$$\mathrm{books},3\mathrm{identical}\mathrm{physics}\mathrm{books},2$$$$\mathrm{identical}\mathrm{chemistry}\mathrm{books}\mathrm{and}2$$$$\mathrm{identical}\mathrm{biology}\mathrm{books}.\mathrm{in}\mathrm{how}\mathrm{many}$$$$\mathrm{ways}\mathrm{can}\mathrm{you}\mathrm{compile}\mathrm{these}\mathrm{books}$$$$\mathrm{such}\mathrm{that}\mathrm{same}\mathrm{books}\mathrm{are}\mathrm{not}\mathrm{mutually}$$$$\mathrm{adjacent}.$$$$\left(anunsolvedoldquestion\right)$$

Answered by cortano1 last updated on 06/Nov/22

$$=\frac{11!}{4!.3!.{(2!)}^2}-{(4!)}^2.3!.{(2!)}^2$$$$=55476$$

Commented by cortano1 last updated on 06/Nov/22

$$\mathrm{o}\mathrm{yes}\mathrm{sir}.\mathrm{thanks}\mathrm{you}$$

Commented by mr W last updated on 06/Nov/22

$$“samebooksarenotmutually$$$${adjacent}^{″}means“notwobooksfrom$$$$thesamekindarenexttoeach{other}^{″},$$$$i.e.leftandrighttoeverybookmust$$$$bebooksfromotherkinds.$$$$youseamtohaveunderstood“notall$$$$booksfromthesamekindare$$$${together}^{″}.$$

Commented by mr W last updated on 06/Nov/22

$$example:$$$$MPMPMPMBCBCisvalid,$$$$MPMPMMPBCBCisnotvalid.$$

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