6 vacas por cada 5 gallinas

If a(0,0,0) and b(2,2,2) are points in coordinate space, how many paths are there from a to b that move from one lattice point to another in the positive x-,y- or z- direction?

The lines shown below are parallel. if the green line has a slope of -1, what is the slope of the red line

This race was first held in 1953 on august 16th. every decade the race finishes with a festival. how many years is this?