Question 35

If $$(n+2)C_8:(n-2)P_4=57:16$$, then n =

Solution

$$(n+2)C_8:(n-2)P_4=57:16$$
$$\Rightarrow$$ $$\dfrac{\dfrac{(n+2)!}{8!*(n-6)!}}{\dfrac{(n-2)!}{(n-6)!}}=\dfrac{57}{16}$$

$$\Rightarrow$$ $$\dfrac{(n+2)(n+1)(n)(n-1)}{8!}=\dfrac{57}{16}$$

$$\Rightarrow$$ $$(n+2)(n+1)(n)(n-1)=57*2520$$

$$\Rightarrow$$ $$(n+2)(n+1)(n)(n-1)=21*20*19*18$$

Therefore, n = 19.

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