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n! = n*(n-1)*n-2......1

$n^{n}$= n*n*n......n

$\frac{n^{n}}{n!}$=$\frac{n*n*n...n}{n*(n-1)*(n-2)*...1}$ This ratio is greater then 1 always for n$\neq 1$

for eg $\frac{3^{3}}{3!} = 4.5$

so $\frac{n^{n}}{n!}\geq 1$

$n^{n}\geq n!$

n! = O($n^{n}$)
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