The Rule of Discarding $1/N_c$ in Inclusive Weak Decays. II

We calculate the leading preasymptotic correction to the inclusive width $b\rightarrow \bar c c s$ (two massive quarks in the final state) due to the operator $\vec \sigma \vec H$. It is found that this correction tends to cancel the $1/N_c$ part of the inclusive width calculated using naive factorization. The absolute value of the effect is of order 0.25. We also discuss how quark-hadron duality is realized in the inclusive decays.