Practice By Tag: Counting Solutions of Linear Equations

1 . Consider the equation $$ x_1 + x_2 + x_3 + x_4 + x_5 = 17. $$ How many solutions $(x_1, x_2, x_3, x_4, x_5)$ does this equation have, where $x_1 \geq 0$, $x_2 \geq 0$, $x_3 \geq 0$, $x_4 \geq 0$, and $x_5 \geq 0$ are all integers?