What is the coefficient of $ a^8b^4c^9d^9$ in $(abc+abd+acd+bcd)^{10}$? I am new to Binomial Theorem and I want to find out the coefficient of $ a^8b^4c^9d^9$ in $$(abc+abd+acd+bcd)^{10}$$ How to find that?

Let us set $abc=D, abd=C, acd=B, bcd=A$. Then $a^8 b^4 c^9 d^9 =A^2 B^6 C D$ and the problem boils down to finding the coefficient of $A^2 B^6 C D$ in $(A+B+C+D)^{10}$, i.e. to counting the anagrams of the word $AABBBBBBCD$. They are
$$ \frac{10!}{2!6!}=\color{red}{2520}.$$
