# Lattice Paths

Probability Level 5

How many $\{(1,1), (1,-1), (2,0)\}$-lattice paths are there from the point $(0,0)$ to the line $x = 8?$

Details and assumptions

A lattice path is a path in the Cartesian plane between points with integer coordinates.

A step in a lattice path is a single move from one point with integer coordinates to another.

The size of the step from $(x_1,y_1)$ to $(x_2,y_2)$ is $(x_2-x_1,y_2-y_1)$.

For a set $S = \{(x_i,y_i)\}_{i=1}^{k}$, an $S$-lattice path is a lattice path where every step has size which is a member of $S$.

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