I wish there was a \(\displaystyle\sum_{x=0}^{n}\) on the left instead!

Calculus Level 5

If the value of the following limit

\[\lim\limits_{n \to \infty} \dbinom{n}{x} \displaystyle\left( \frac{m}{n}\right)^{x}\displaystyle\left( 1-\frac{m}{n}\right)^{n-x}\]

for \(x=5\) and \(m=5\) is \(S\), evaluate \(\left \lfloor{1000S}\right \rfloor\).

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