Question

Solve the following inequalities.
$2C_5^n>11C_3^{n-2},nϵN$

Answer 1

$2C_5^n>11C_3^{n-2},nϵN$

$\therefore 2\times \frac{n(n-1)(n-2)(n-3)(n-4)}{5\times 4\times 3\times 2\times 1}>11\times \frac{(n-2)(n-3)(n-4)}{3\times 2\times 1}$

$\therefore \frac{2n(n-1)}{20}>11$

$n(n-1)>110$

$n^2-n-110>0$

$(n-11)(n+10)>0$

$\therefore nϵ(-\infty ,-10)\cup (11,\infty )$