Evaluate ∭EzdV\iiint_E z dV∭EzdV where EEE is the region in the first octant bounded by x+y+z=1x+y+z=1x+y+z=1.
16\frac{1}{6}61
124\frac{1}{24}241
112\frac{1}{12}121
148\frac{1}{48}481