Medium

Probability

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?

Notes

Hint