Macrostates of 6 F-D particles? (Answer key wrong?)

[Lagraaaange]

Homework Statement

For six indistinguishable particles obeyed Fermi Dirac statistics where multiplicity, Ω = 162, g = 3 (degeneracy), U = 7
a. Find the total number of macro states.
Answer in book: 8. Idk why
b. Calculate the thermodynamic probability, W of each macro state.
d. Find the average occupation number of each state
Answer: 2.27,1.722,1.056,0.667,0.0222,0.056
BOOK MIGHT BE WRONG.

Homework Equations

W = ∏(over j) gj! / (gj-Nj)!Nj!
<Nj> = Ω^-1 * ∑(over k) NjkWk

The Attempt at a Solution

I drew out 6 macro states.
I got thermo prob of 9, 27, 9,81,9,9 and the occupation numbers didn't match up.

 

[Lagraaaange]

SOLVED. Made mistake in drawing of macro states.