(Canadian Senior Mathematics Contest 2024, Part A, Question 3, CEMC - UWaterloo)

At the end of yesterday’s soccer game between Team Why and Team Zed, Team Why had scored $3$ goals and Team Zed had scored $2$ goals. At half-time of the game, Team Why had scored $y$ goals and Team Zed had scored $z$ goals. If $y \geq 0$ and $z \geq 0$, how many possibilities are there for the ordered pair of integers $(y, z)$?

(In soccer, each team’s score is always a non-negative integer that never decreases as the game proceeds.)