If C 6 ? n + 2 P 2 ? n - 2 = 11 , then n satisfies the equation

Question

If $\frac{{}^{n + 2}C_{6}}{{}^{n - 2}P_{2}} = 11$ , then $n$ satisfies the equation

Smart Achievers · Accepted Answer

(3)

$We have,$ $\frac{{}^{n + 2}C_{6}}{{}^{n - 2}P_{2}} = 11$

$\Rightarrow$ $\frac{(n + 2) (n + 1) n (n - 1)}{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 11$

$\Rightarrow$ $(n + 2) (n + 1) n (n - 1) = 11 \cdot 10 \cdot 9 \cdot 8 \Rightarrow n = 9$

$Now, n = 9 satisfies only n^{2} + 3 n - 108 = 0$

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