Multinomial coefficients

#multinomial#coefficient#expansion

Statement

Find the coefficient of $a^2bc$ in $(a+b+c)^4$ .

Hint

Use multinomial: $\binom{4}{2,1,1}$ .

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Multinomial. $\binom{4}{2,1,1}=\frac{4!}{2!\,1!\,1!}=12$ .

Conclusion. The coefficient is $12$ .