medium Probability
A release-checked medium problem for training Combinatorics.
You are playing a 2D game where your character is trapped in a $6 \times 6$ grid. Your character starts at $(0,0)$ and can only move up and right. There are two power-ups located at $(2,3)$ and $(4,6)$. How many possible paths can your character take to get to $(6,6)$ such that it can collect at least one power-up?
This Probability problem is tagged Combinatorics. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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