Help ASAP plz

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?

Look at this pattern ; 1,4,9, number 10000 belongs in this pattern . what’s the place of this number?

Michael is training for a marathon. in his first week he plans to run 8miles. what path should he take