If ^ (n+2) P_ 3 :^ (n+1) P_ 3 =10: 7 then find n. - Vidyadip

Question

If $^{(n+2)} P_{3}:^{(n+1)} P_{3}=10: 7$ then find $n$.

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Answer

$\frac{{}^{(n+2)}{P_{3}}}{{}^{(n+1)}{P_{3}}} =\frac{10}{7}$
$\therefore \frac{(n+2)(n+1)(n)}{(n+1)(n)(n-1)}=\frac{10}{7}$
$\therefore \frac{n+2}{n-1}=\frac{10}{7}$
$\therefore 7(n+2)=10(n-1)$
$\therefore 7 n+14=10 n-10$
$\therefore 3 n=24$
$\therefore n=8 $

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