Question: 2014 Fall Midterm - 8

Author: Michiel Smid

How many solutions are there to the equation $x_1 + x_2 + x_3 + x_4 = 27$, where $x_1 \geq 0$, $x_2 \geq 0$, $x_3 \geq 0$, and $x_4 \geq 0$ are integers?

a) ${30 \choose 3}$

b) ${30 \choose 4}$

c) ${31 \choose 3}$

d) ${31 \choose 4}$

How many solutions are there to the equation $x_1 + x_2 + x_3 + x_4 = 27$, where $x_1 \geq 0$, $x_2 \geq 0$, $x_3 \geq 0$, and $x_4 \geq 0$ are integers?

(a)

${30 \choose 4}$

(b)

${31 \choose 4}$

(c)

${30 \choose 3}$

(d)

${31 \choose 3}$