Question: 2018 Fall Midterm - 5
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?
(a)
${21 choose 5}$
(b)
${22 choose 4}$
(c)
${21 choose 4}$
(d)
${22 choose 5}$