, 2011

An ordered list of four numbers is called a quadruple. A quadruple $(p, q, r, s)$ of integers with $p, q, r, s \geq 0$ is chosen at random such that $2p + q + r + s = 4$. What is the probability that $p + q + r + s = 3$?

(A) $\frac{3}{22}$ (B) $\frac{3}{11}$ (C) $\frac{3}{19}$ (D) $\frac{6}{19}$ (E) $\frac{2}{7}$