If-n-2-C-8-n-2-P-4-57-16-then-the-value-of-n-is-

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

If^{n + 2} C_{8} :^{n - 2} P_{4} = 57 : 16, then the value

of n is \dots \dots

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) (n) (n - 1) = 143640

\Rightarrow n = 19

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