binomial limit when limit approches to infinity $\displaystyle \lim_{n\rightarrow\infty}\binom{n}{x}\left(\frac{m}{n}\right)^x\left(1-\frac{m}{n}\right)^{n-x}$
solution i try 
$\displaystyle \lim_{n\rightarrow\infty}\left(\frac{m}{n}\right)^x\left(1-\frac{m}{n}\right)^{n-x}=\lim_{n\rightarrow\infty}(\frac{m}{n}+1-\frac{m}{n})^n=1$
I have edited my post 
This is wrong how i find right answer. Help me

Note that we have
$$\binom{n}{x}\left(\frac{m}{n}\right)^x\left(1-\frac mn\right)^{n-x}=\frac{m^x}{x!}\left(1-\frac{1}{n}\right)\left(1-\frac{2}{n}\right)\cdots\left(1-\frac{x-1}{n}\right)\left(1-\frac mn\right)^{n-x}$$
Therefore, for fixed $x$, we have 
$$\lim_{n\to \infty}\binom{n}{x}\left(\frac{m}{n}\right)^x\left(1-\frac mn\right)^{n-x}=\frac{m^x}{x!}e^{-m}$$
