[SOLVED] Moment generating function of the Binomial distribution

*Suppose that $\displaystyle Y~Bin(n,p)$, with probability mass function given by*

*$\displaystyle p_Y(y)=P(Y=y)=\left( \begin{array}{c}n \\ y \end{array} \right) p^y(1-p)^{n-y}, y=0,1,...,n$*

*and $\displaystyle 0$ otherwise. **Show that the moment generating function of $\displaystyle Y$ is given by*

*$\displaystyle M_y(t)=\{pe^t+(1-p)\}^n$*

I keep getting majorly lost with this. I've tried Googling to find a solution to this, since it's a fairly generic question, but to no avail. Can anyone show me how to show this?