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Question Number 112934 by mr W last updated on 10/Sep/20

$$\mathrm{There}\mathrm{are}4\mathrm{identical}\mathrm{mathematics}$$$$\mathrm{books},2\mathrm{identical}\mathrm{physics}\mathrm{books},2$$$$\mathrm{identical}\mathrm{chemistry}\mathrm{books}\mathrm{and}2$$$$\mathrm{identical}\mathrm{biology}\mathrm{books}.\mathrm{in}\mathrm{how}\mathrm{many}$$$$\mathrm{ways}\mathrm{can}\mathrm{you}\mathrm{compile}\mathrm{the}10\mathrm{books}$$$$\mathrm{such}\mathrm{that}\mathrm{same}\mathrm{books}\mathrm{are}\mathrm{not}\mathrm{mutually}$$$$\mathrm{adjacent}.$$

Commented by I want to learn more last updated on 11/Sep/20

$$\mathrm{MMMM}\mathrm{PP}\mathrm{CC}\mathrm{BB}$$$$4!\times 4!\times 2!\times 2!\times 2!$$$$\mathrm{sir}\mathrm{i}\mathrm{just}\mathrm{tried}$$

Commented by I want to learn more last updated on 11/Sep/20

$$\mathrm{Ohh},\mathrm{i}\mathrm{did}\mathrm{the}\mathrm{same}\mathrm{book}\mathrm{must}\mathrm{be}\mathrm{together}.$$$$\mathrm{That}\mathrm{is}\mathrm{the}\mathrm{one}\mathrm{am}\mathrm{familier}\mathrm{with}[\mathrm{sir},\mathrm{this}\mathrm{one}\mathrm{is}\mathrm{new}\mathrm{to}\mathrm{me}.$$$$\mathrm{I}\mathrm{would}\mathrm{love}\mathrm{to}\mathrm{learn}\mathrm{it}\mathrm{sir}$$

Commented by I want to learn more last updated on 11/Sep/20

$$\mathrm{I}\mathrm{will}\mathrm{wait}\mathrm{for}\mathrm{it}.\mathrm{Thank}\mathrm{you}\mathrm{sir}.$$

Commented by mr W last updated on 12/Sep/20

$$basicallythesameasQ109387$$

Commented by I want to learn more last updated on 14/Sep/20

$$\mathrm{Sir},\mathrm{please}\mathrm{study}\mathrm{the}\mathrm{principle}\mathrm{of}\mathrm{inclusion}/\mathrm{exclusion},\mathrm{it}\mathrm{will}\mathrm{help}\mathrm{you}.$$$$\mathrm{here}.\mathrm{I}\mathrm{believe}\mathrm{you}\mathrm{will}\mathrm{understand}\mathrm{some}\mathrm{principle}\mathrm{there}\mathrm{better}\mathrm{than}\mathrm{me}\mathrm{sir}.$$$$\mathrm{riomicheal}\mathrm{is}\mathrm{trying}\mathrm{to}\mathrm{use}\mathrm{it}\mathrm{too}\mathrm{but}\mathrm{he}\mathrm{cannot}\mathrm{proceed}.$$$$\mathrm{n}({\mathrm{M}}^{\prime }\cap {\mathrm{P}}^{\prime }\cap {\mathrm{C}}^{\prime }\cap {\mathrm{B}}^{\prime })$$

Commented by mr W last updated on 14/Sep/20

$$theprincipleiseasytounderstand.$$$$buti{don}^{\prime }tthinkithelpsherereally.$$

Commented by Tawa11 last updated on 15/Sep/21

$$\mathrm{nice}$$

Answered by Rio Michael last updated on 10/Sep/20

$$\mathrm{Allow}\mathrm{me}\mathrm{to}\mathrm{present}\mathrm{an}\mathrm{idea}\mathrm{i}\mathrm{had}\mathrm{ones}\mathrm{seen}\mathrm{a}\mathrm{studied}.$$$$\mathrm{If}\mathrm{we}\mathrm{say}A\mathrm{is}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{arragments}\mathrm{where}\mathrm{mathematics}\mathrm{books}$$$$\mathrm{are}\mathrm{adjacent},B\mathrm{is}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{arrangments}\mathrm{where}\mathrm{Physics}\mathrm{books}\mathrm{are}$$$$\mathrm{adjacent},C\mathrm{is}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{arrangments}\mathrm{where}\mathrm{chemistry}\mathrm{books}\mathrm{are}$$$$\mathrm{adjacent}\mathrm{and}D\mathrm{is}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{arrangments}\mathrm{where}\mathrm{biology}\mathrm{books}$$$$\mathrm{are}\mathrm{adjacent}.\mathrm{then}\mathrm{the}\mathrm{answer}\mathrm{we}\mathrm{need}\mathrm{is}$$$$n(A{}^{\prime }\cap B^{\prime }\cap C{}^{\prime }\cap D^{\prime }).$$$$\mathrm{i}\mathrm{will}\mathrm{figure}\mathrm{out}\mathrm{how}\mathrm{to}\mathrm{get}\mathrm{this}\mathrm{value}.$$

Commented by I want to learn more last updated on 11/Sep/20

$$\mathrm{Am}\mathrm{still}\mathrm{waiting}\mathrm{for}\mathrm{your}\mathrm{work}\mathrm{sir}.\mathrm{Thanks}$$

Commented by Rio Michael last updated on 14/Sep/20

$$\mathrm{am}\mathrm{finding}\mathrm{difficulties}\mathrm{in}\mathrm{computing}$$$$\mathrm{my}\mathrm{answer},\mathrm{been}\mathrm{on}\mathrm{this}\mathrm{for}\mathrm{long}\mathrm{now}$$

Commented by I want to learn more last updated on 14/Sep/20

$$\mathrm{And}\mathrm{me}\mathrm{too},\mathrm{that}\mathrm{was}\mathrm{why}\mathrm{i}\mathrm{said}\mathrm{he}\mathrm{should}\mathrm{study}\mathrm{it},\mathrm{he}\mathrm{can}\mathrm{understand}$$$$\mathrm{it}\mathrm{better}.$$

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