I've calculated density matrix
$$ rho_{ABC} = \frac{1}{2} \left( \left| 100 \right\rangle \left\langle 100 \right| + \left| 100 \right\rangle \left\langle 001 \right| + \left| 001 \right\rangle \left\langle 100 \right| + \left| 001 \right\rangle \left\langle 001 \right| \right)$$
and ##...