Example 1.5.3.
How many integer solutions are there to the equation
\begin{equation*}
x_1 + x_2 + x_3 + x_4 + x_5 = 13\text{.}
\end{equation*}
(An integer solution to an equation is a solution in which the unknown must have an integer value.)
where \(x_i \ge 0\) for each \(x_i\text{?}\)
where \(x_i > 0\) for each \(x_i\text{?}\)
where \(x_i \ge 2\) for each \(x_i\text{?}\)