Consider a stock, whose value is assumed to change each day according to the following probability distribution:

$Z=\{\begin{array}{ccc}3,& \text{w}\text{i}\text{t}\text{h}\text{p}\text{r}\text{o}\text{b}\text{a}\text{b}\text{i}\text{l}\text{i}\text{t}\text{y}& \frac{1}{3}\\ 0,& \text{w}\text{i}\text{t}\text{h}\text{p}\text{r}\text{o}\text{b}\text{a}\text{b}\text{i}\text{l}\text{i}\text{t}\text{y}& \frac{1}{3}\\ -2,& \text{w}\text{i}\text{t}\text{h}\text{p}\text{r}\text{o}\text{b}\text{a}\text{b}\text{i}\text{l}\text{i}\text{t}\text{y}& \frac{1}{3}\end{array}$

Let $x_n$ denote the stock price at day $n$ and $x_0=100.$

$1.$ Calculate how many possible combination Xn in the first $4$ days such that X$3>=104$

$2.$ Calculate Pr$($X$4>=104)$