Practice By Tag: Counting Solutions of Linear Equations

Question: 2018 Winter Midterm - 9

1 . Consider the equation $$ x_1 + x_2 + x_3 + x_4 = 33, $$ where $x_1 \geq 0$, $x_2 \geq 0$, $x_3 \geq 0$, $x_4 \geq 0$ are integers. How many solutions does this equation have?

(a)

${37 \choose 3}$

(b)

${36 \choose 4}$

(c)

${37 \choose 4}$

(d)

${36 \choose 3}$