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Question Number 80777 by zainal tanjung last updated on 14/Feb/20

$$\mathrm{If}{}^{n+2}{C}_8:{}^{n-2}{P}_4=57:16,\mathrm{then}\mathrm{the}\mathrm{value}$$$$\mathrm{of}n\mathrm{is}......$$

Answered by Joel578 last updated on 06/Feb/20

$$\frac{(n+2)!}{8!(n-6)!}:\frac{(n-2)!}{(n-6)!}=\frac{57}{16}$$$$\Rightarrow \frac{(n+2)!}{8!(n-6)!}\times \frac{(n-6)!}{(n-2)!}=\frac{57}{16}$$$$\Rightarrow (n+2)(n+1)\left(n\right)(n-1)=143640$$$$\Rightarrow n=19$$

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