I need to integrate over the region in the title 0 < x < y < z < 1.

Am I correct in understanding that this is the region in x,y,z-space in the first octant with vertex interceptions at (1,0,0), (0,1,0), and (0,0,1) resembling a "pyramid"?

But then the integral of 48*x*y*z over this region must equal one, but I am getting

The integral from x=0 to 1, the integral from y=0 to 1-x, the integral of z=0 to 1 - x - y of 48xyz dz dy dx (this is a triple integral written in "word" form since I don't know latex.

But my answer is 1/15, which is not correct. What am I doing wrong? Thanks!