There-are-4-identical-mathematics-books-3-identical-physics-books-2-identical-chemistry-books-in-how-many-ways-can-you-compile-the-9-books-such-that-same-books-are-not-mutually-adjacent-

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Question Number 113368 by mr W last updated on 12/Sep/20

$$\mathrm{There}\mathrm{are}4\mathrm{identical}\mathrm{mathematics}$$$$\mathrm{books},3\mathrm{identical}\mathrm{physics}\mathrm{books},2$$$$\mathrm{identical}\mathrm{chemistry}\mathrm{books}.$$$$\mathrm{in}\mathrm{how}\mathrm{many}\mathrm{ways}\mathrm{can}\mathrm{you}\mathrm{compile}$$$$\mathrm{the}9\mathrm{books}\mathrm{such}\mathrm{that}\mathrm{same}\mathrm{books}\mathrm{are}$$$$\mathrm{not}\mathrm{mutually}\mathrm{adjacent}.$$

Answered by mr W last updated on 15/Sep/20

$$case1:$$$$xMxMxMxMx$$$$\Rightarrow \frac{5!}{3!2!}=10ways$$$$$$$$case2:$$$$xMxMxyMxM$$$$\Rightarrow 4\times 2\times \frac{3!}{2!}=24ways$$$$$$$$case3:$$$$MxMxyMxMx$$$$\Rightarrow 4\times 2\times \frac{3!}{2!}=24ways$$$$$$$$case4:$$$$MxMxyMxyM$$$$\Rightarrow 3\times 2\times 2=12ways$$$$$$$$case5:$$$$MPMPCPMCM$$$$MCMPCPMPM$$$$MPMCPCMPM$$$$\Rightarrow 3\times 3=9ways$$$$$$$$totally:10+24+24+12+9=79ways$$

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