Find the Coefficient of $x^8$ by Multinomial Theorem Expansion for $(1+x^2-x^3)^9$

Question

Problem: Find the coefficient of the term $x^8$ for the expansion of $(1+x^2-x^3)^9$
Attempt:
By the multinomial theorem: $$(1+x^2-x^3)^9=\sum_{b_1+b_2+b_3=9}{9\choose b_1,b_2,b_3}(1)^{b_1}(x^2)^{b_2}(-x^3)^{b_3}$$ This means a general term for the expansion of $(1+x^2-x^3)^9$ will be in the form of ${9\choose b_1,b_2,b_3}(1)^{b_1}(x^2)^{b_2}(-x^3)^{b_3}$
We achieve $x^8$ by letting $b_1=5,b_2=4,b_3=0$, it follows that: $${9\choose 5,4,0}(1)^{5}(x^2)^{4}(-x^3)^{0}=126x^8$$ My Question:
The actual answer is $378$, what am I missing?