First of all, I am not quite sure but I think the problem asks for a permutation/combination of 13 elements over the {x, y, z} set.
Here is the problem: How many ways are there for a spaceship to travel in a 3-D space from the origin (0,0,0) to the point (2,4,7) by taking 13 steps, one at a time, where a step moves one unit in the positive x, y or z direction? Moving in the negative x, y or z direction is prohibited.
Thank you very much in advance!