Willy Walks to School (Part I)
Willy lives in the Cartesian Coordinate Plane. Willy's house lies at \( (0,0) \), while his school, Takoma Park, lies at \( (10,12) \). Willy needs to walk to school in the shortest way possible, else, he will be late to school and will receive three warnings from Mr. Siddique. How many ways are there to get from the origin to \( (10,12) \) moving only up and to the right?
(Note that Willy must walk on the roads, or parallel to the \(x\)- or \(y\)-axis - if he is caught not doing so, he will receive three warnings.)